So like Friendlysociopath used, I will be borrowing from anime to answer.

A Certain Scientific Teleporter

In the series A Certain Magical Index and A Certain Scientific Railgun we're introduced to a character who can teleport. They're a part of a neighborhood watch-like program (so they don't go about killing people) but they have an unusually high combat incident count. Their main line of attack is to teleport metal darts into the clothes of opponents and pin them to surfaces. Usually they knock them against the surfaces first (satisfying a more narrow application of the "Must have visited this place before" clause). But they have a brevity of application to their powers.

1. They can teleport objects into people. So if you're a teleporter looking to just end any 1v1 engagement, teleport a needle into their heart or brain. Done. Assuming the "visited this place before" means only that you've physically seen it. But if we're more specific (e.g. you've had to have touched the place before") then we still have the standard option of restraining people with heavy objects once you've touched them.




2. They can teleport material into structural supports and bring down buildings. Again, assuming you just have to physically have seen your target place before then you can just teleport glass panes from a building's windows to their structural supports and down goes a couple hundred million dollars not to mention the mass panic. Although, this involves changing the orientation of an object in teleportation. Another limitation. But if you have to touch all of the target you're teleporting to then bringing down buildings is a little out of reach. However, you can still cause mass panic because...



3. 
   

   You can teleport double your mass to the tops of buildings and have them come crashing down. 140kg dropping 20 stories will hurt a great deal. Again, if you only have to have seen the target, dropping 140kg asphalt balls from the cloud line will be incredibly damaging depending on cooldown times or other physical limitations. The character in question doesn't do this but a Rival teleporter does try to do this to crush the character.

   
   
   

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So you have options in combat when it comes to being a teleporter. As others have said you can really abuse the rule and win a lot of fights just by sending an opponent free solo skydiving or jamming their own weapon into their brain. On a less lethal note, dropping 140kg's of sand on someone will buy you time to incapacitate them or kill them. Teleporting 140kg's of industrial staples will pin someone to a surface or fewer metal stakes will do the same. Even just threatening teleporting a needle into someone's brain will stop a lot of fights.

Against groups, like IT Alex stated, teleport them away till you get down to a manageable number then start incapacitating or killing as you see fit. If you have to fight full groups, hope for the environment to be in your favor and teleport holes into the ground in front of people and use that dirt to cover someone. Or start throwing javelins at people.

And if you're just in it for the mass panic, you have too many options to count. You can't blow up cities but you can royally mess with them. Teleport small pieces of bridge supports away, drop asphalt boulders from on high, ruin electrical substations, even destroy buildings. You can cause quite a bit of damage in a very short amount of time with little effort.

The Teleporter can teleport themselves and/or any object (including people) they are touching, with a total mass limit of roughly double their own mass
People/things/self can only be teleported to places which the Teleporter has previously visited in person

If you've ever watched Darker Than Black the protagonist faces someone with a teleportation power. Except instead of teleporting themselves they teleport a fist-sized bunch of matter- which they typically use to swap pieces of building with the heart of the person they're trying to assassinate.

Air Drop

In X-men: First Class, a guy with Nightcrawler's powers kills people by teleporting into the air with them and then dropping them while he teleports back down. Since he can teleport right up to someone to grab them, there isn't much defense against this. You specify only places he has been, but as long as he's gone skydiving even once, this shouldn't be a problem.

(Others mentioned that specific attack in the comments section. I just noticed, even thought they posted before I did. Credit should go to @Willk and @BKLassen. Or, should I just delete that part?)

Partial Teleport

If your teleporter doesn't need to take the whole object or person with him, he could put his hand on a guy, and teleport away with only part of them. Instant decapitations, or 'Disarming'.

Well, one less lethal thing no one else has pointed out is instant incarceration. The teleporter visits a jail cell or a bank vault, which is then locked. The teleporter doesn't even need to be let out, of course, because they can take themselves out at any time.

Once in conflict with someone, the teleporter need only touch their opponent to teleport them away, into the locked cell or vault. (Go to jail. Go directly to jail. Do not pass Go. Do not collect $200.)

For a more lethal version, the teleporter need only enter an incinerator when it's not on, and then have it fired up after they leave. (Tap. You're toast.) This idea could be extended to any dangerous environment where the danger can be easily turned off and on: inside an nuclear reactor, directly above an industrial metal shredder, a large container filled with acid or toxic gas, etc. Heck, the teleporter could even go in a deep sea submarine once, and then teleport people to the bottom of the ocean.

Unfortunately, the limitation of places he can teleport to by having to have been there at some point makes him a better defensive fighter than an offensive. Having sufficient time to prepare, he can literally attack from anywhere within an area.

One on One.

Your teleporter should teleport twice his mass in an entangling object over a wide area (nets, barbed wire, fishing line) to immobilize his opponent. Then, teleport a pointy weighted object on top of them. Having been entangled they will have a hard time dodging and each dodge they succeed will make them more entangled and less able to dodge the next one. Alternatively, teleport behind them and touch them to teleport them to a location that you have sky-dived (without a parachute).

Multiple opponents.

Survival should be paramount in a one on many fight. Teleport and touch a combatant and put them literally anywhere other than the fighting location until it is 1v1. You could even use the mid-air approach from previously. The key is to not fight disadvantageous fights and instead make every fight fair or in your favor.

Mass Destruction.

No more so than the average person. The only caveat is that what would normally be a suicide attack for most people is now survivable via teleportation.

Most people would be unable to track and/or stop your teleporter. If he can teleport as fast as he can think then he would be able to (with practice) eliminate people within seconds.

My answer works on Three assumptions:

1: The person using the teleportation power can teleport parts of a object he/she is touching.

And/Or

2: There is little/no cool-down in-between teleportation attempts.

And/Or

3: If the teleporter can choose how precise the "location he has been" part is.

Most organisms cannot function in combat without a brain. So if assumption #1 is correct, then you can not only quickly kill them, but also merely incapacitate them by removing things such as clothing, weapons, limbs, or possibly just all the air in their lungs.

All people need a defense, whether it is armor, wits, luck, or a combination of said three. Teleporters have a fourth if assumption #2 works: By constantly teleporting the area near them away, you create what essentially is a wormhole that they control in order to not only prevent damage, but maybe also send the damage right back at the aggressors!

If you have in combat and holding a sword (example item), you could teleport the hilt of the sword right next to the opponent's forehead, with the blade orientated towards the brain. Voila! Sword has now been stabbed though whatever armor the guy has, and is now in the brain.

This answer focuses on on-on-one and can be extended to one-on-multiple.

This power would be extraordinarily useful. Anywhere this person has ever been, they can make "anything they touch" appear there.

Convenient death trap: arrange to send folks to kill zones

Make an expedition to the North Pole (which will kill probably even many supers unprepared to be sent there in very short order). Take an airplane ride with a window seat, then simply teleport anyone the person wants to get rid of there.

Or just get a secret lair. Build a sub-sub basement. Surround it with chain link fencing, then flood it with water. Teleport people there to drown. Much less public that way. People just disappear and aren't found in spectacular, publicity-generating ways (like falling out of the sky randomly over the Midwest, or a huge pile of people killed via exposure being found at the North Pole).

If the user doesn't want to kill their enemies, and has resources, like they're Batman, build a prison. Hire a bunch of superpowered guards. Spend a few minutes locked inside a 2-foot by 2-foot square closet surrounded by powerproof glass, and you've got an intake cell where your new inmate materializes. Repeat, and you can handle multiple incoming bad (or I suppose good) guys simultaneously.

Anywhere the user has, or might have ever, been is not secure

Anywhere they can break into, or might have ever broken into, is not secure. Any place they might have flim-flammed their way past the front desk in disguise (think civvies), even briefly, is not secure. Any place they've ever worked cannot be considered secure. Note that the list of such places is vast because you won't know where they've been. This remains true as long as they live.

They can take a tour of the White House, even the unsecured parts, in disguise. Twenty years later, they could decide 'screw this, time to assassinate the President' and now you've got a problem. They can take a job as the janitor of an office building where someone they're targeting works. Failing everything else, they take a job working for these guys and then pretty much learn how to get anywhere they want.

Seriously, watch the video, it exposes how much even 'secure' locks mostly aren't. All this person needs to do is pop a door when nobody's around, or maybe when people are around and you just do the 'elevator repairman' schtick (again from the video).

TL;DR - This person can get almost anywhere. And if they can, then anyone who can engage their services can also. If you want in, and either can pay, or convince them to help you, a plan can almost certainly be arranged to give the teleport user the ability to get your entire crew in. This person can also assassinate a lot of folks by finding their office, then teleporting hand grenades or nerve gas canisters or even assassin droids in.

Devastating force multiplier

Combat effectiveness is not all about kicking ass and taking names. Some things don't directly bring the thunder, but are good at making the thunder your other folks have got more effective. The military has a name for this; they call it a force multiplier.

In addition to the direct usefulness of teleportation in a fight (being untouchable, being able to kill at a distance, being able to take people prisoner just by touching them, etc) teleportation is a devastating force multiplier.

The way you have set this up, teleportation is a highly effective force multiplier, because the teleporter can bring a whole team of capes along for the ride. And they can get to the scene much quicker than if they had to take the Batplane or whatever. As established above, if the teleporter spends a lot of their time travelling around, considering it their job to spend a lot of their 'off' time expanding their potential teleportation destinations, they (and their backup) will be able to almost instantly appear to disrupt the plans of their adversaries.

Instead of being able to count on it taking (say) between 20 minutes and an hour after the alarm goes off, until the Superfriends show up (because even if they're all on duty right that second they still have to physically go to the place), with Mister Panopticon on their side, they can appear in under a minute. I.e. if you want to attack something they care about defending, you have to assume they will be on you immediately. Smash-and-grabs, where the idea is you're gone before anyone shows up, are out.

Likewise, if the Superfriends want in, you have to assume they can get in anytime they want with no warning. They will simply teleport a whole crew of heavy-hitters somewhere inside your security perimeter. You can't rely on being able to buy time, keeping them tied up at the front door so they don't get into the sensitive parts of your facility. You can't really have a security 'perimeter', you have to have very high security basically throughout any facility you want to keep these folks out of,.

Other answers have covered fairly well the options for one to one combat, and even vs groups. This answer poses a solution to mass destruction.

The only restriction is enabling partial teleportation.

Here's a few ideas, depending on how extreme you want to go.

1) Shockwaves. Teleportation should always produce a shockwave. Consider, what happens to the air that used to occupy the space the teleported object now does? As you've defined the ability (must be touching thing to teleport) they could not possibly swap the air and the teleported object. So the air must remain, pushed out at hyper velocity by the sudden presence of something teleporting in. Boom, shockwave!

2) Since you are already moving matter out of the way (air) what happens if you teleport an object into something more... substantial? Imagine teleporting a 200 pound block directly into the same space already occupied by another 200 pound block. A rather impressive explosion should result as most of the chemical bonds in whatever used to be there are suddenly broken all at once. At the very least, it generates a shockwave as before, only with a large amount of shrapnel mixed in.

3) Let's take his to the logical extreme: use simulations partial teleportations to compress an object down to a single point. Literally. Depending on how precise and accurate your teleporter can be, this should result in a nuclear explosion, as the an entire 200 pounds of atomic nuclei are forced into the same space, destabilizing them and causing them to break up. This should result in a nuclear explosion. Depending on material teleported, it may just result in irradiating the surrounding area with exotic particles (you might even want this outcome, kill the people, leave the buildings...). Alternatively, it also might form a black hole and destroy the Earth. Be careful with this one...

As a disclaimer, I haven't run the numbers on any of these situations. They just seem like logical consequences based on my understanding of physics. I'm be happy to be corrected if someone else cares to do so.

Flechettes as anti-personnel weapons

Your best bet for taking out groups of individuals in the open in a dead-simple way is WW1's air-dropped flechettes:

They weighed about 20g each, so you could easily teleport a box of about 7,000 of 'em up into the sky above whoever's day you want to ruin:

They're pretty effortlessly lethal over an area of a few hundred square yards.

And unlike the poor airplane pilots, you don't have one box of 'em, you have as many as you need. And if custom flechettes are out of your budget, just teleport boxes of nails. Those are free w/crime. :P

The question of what happens to the atoms at the destination of the teleport when the person appears. Clearly they must at the very least be moved out of the way, if not exchanged (i.e. moved to the place where the teleporting person came from) or destroyed.

That makes merely teleporting into the space where a person or object is a powerful weapon, as all or part of them will be instantly displaced.

A lot of cool answers here. I was thinking in little different approaches.

Reactive components

You can have two recipes of chemicals not dangerous but reactive between each other. (like metal and chlorine, for example) And just teleport with both hand in the face of your enemies.

No hands

You can have some flammable liquid, like gasoline, in a camelbak, and just suck it and teleport it with your tongue. Now you only need some type of ignition. (Maybe like in the previous point)

Sand, gravel or any amount of small objects

You only can teleport something of double your mass, but one grain of sand or a little peeble it's ok. Now... put your hands on the ground and you basically can start a nonstop rain of sand, gravel, stones or whatever.

Same but with water

Same as before. One drop of water is nothing and you are basically able to flood a fucking country with the water of a sea. That's a massive destruction.

Consider the original Jumper book, not the Hollywood mess. In the book his teleportation is limited to what he is carrying.

He uses it for combat in two ways:

1) Grab someone, tip back (so their feet come off the ground) and teleport next to a cliff (in the book he can only teleport to where he's been or where he can see) next to water. Let go, teleport away. If you want a lethal combat option (he didn't) the same idea but without water.

2) Swing a weapon, teleport while it's swinging.

simply calculate the coordinates of where your enemy is and teleport a screw or any other object to his neck

Teleportation in gradually increasing stages:

This answer aims to complement other answers by mentioning how the ability to teleport can progress in methodology and power. The assumed limits are: Mass is limited related to the users' mass (twice the mass as baseline), can only teleport to places one visited.

1. Self-Teleportation: The user can teleport himself in and out of combat. He'd use weapons and the environment to his advantage. Requires preparation by visiting the area. Nice for retreat and utility, not really effective in combat.




2. Teleport objects and others: The user can teleport others he touches. Still needs to get close to the target and touch it for a sufficient time (which would be the main difficulty). But this is a potential kill move already.




3. Able to negate and redirect (but not create) kinetic forces. Allows jumping off cliffs and teleporting without suffering fall damage. With enough training it would allow flight, by redirecting falling momentum.




4. Increase teleportation range beyond touch by connection via air - which requires an understanding how to teleport gases. Efficiency diminishes over distance and air density.




5. Able to teleport other objects not only by touching, but with any body contact. In addition the required teleportation time could become near instant. Able to protect oneself by teleporting incoming projectiles away or even reflecting them.




6. Grasping how and why objects can only be teleported as whole objects, and surpass that limitation by learning that with enough force applied objects can be ripped apart via teleportation, effectively toying with atomic/molecular bonds itself.




7. Ability to increase the "already visited" area by focussing and expanding it through vision, however rather slowly.




8. Instead of only being able to negate momentum, the user harnesses the ability to negate cosmic forces working all around the universe in a local area, effectively speeding up objects locally upon teleportation to potentially extreme velocity in any direction. This would weaponize relatively small objects to devastating projectiles melting themselves through anything and creating apocalyptic explosions.

I don't know, that sounds overpowered and a bit silly. Teleportation with limits is much more interesting. Like not being able to teleport others out of danger, or not being able to teleport sufficiently far away or more than a few times in quick succession. In Project Horizons there was a character who would teleport behind someone, stab them with a sword, grab their gun and shoot their buddy, use them as a shield, teleport above another guy, crash stomp them, shoot another guy in the head, drop a grenade and teleport out the door and stroll away all while singing a happy song.