From the Basic Rules section on Concentration:

Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends.

If a spell must be maintained with concentration, that fact appears in its Duration entry, and the spell specifies how long you can concentrate on it. You can end concentration at any time (no action required).

The rule is very short and only says "at any time (no action required)". How this "any time" is defined?

An example scenario:

I cast levitate on an enemy to remove them from the battle. Later at his turn, it turns out that he brings a crossbow. The DM declares the attack, but then I interrupt him and say that I end my concentration, so he will fall down and become prone.

Another example scenario:

I cast levitate on myself and fly 30 ft. The enemy then flies and spends all his movement to fly to me to attack me in melee. After he reaches me, I declare ending my concentration, so I can fall back to the ground, preventing him to attack me.

Is this allowed? Can I end concentration conveniently any time, interrupting any currently declared action/event?

You can end concentration at any time (no action required).

As it says above, you can end it at any time, no action required. It means you don't need to use a reaction, so you can elect to just end it.

Which means yes, you can end your concentration as an enemy approaches so that you drop out of their reach.

You can end concentration at any time (no action required)

but

The DM will decide how it affects already declared actions.

Rule of Cool may let you use this trick once or twice to avoid attacks - but your DM can prevent you from abusing this :

1. There is no "stack" in DnD, as opposed to Magic the Gathering. You don't interrupt, and act first. Once that crossbow shot / charge has been declared and you respond with ending concentration, it's up to the DM to decide in which order those should be resolved.


2. Rules state that free fall (from less than 100m) is resolved instantaneously... but do not specify anything regarding "floating gently to the ground" - which makes you an easy target, as you don't exert control on your movement.

To interrupt another character's turn usually takes a Reaction

The problem here is that the game's mechanical means to interrupt another's turn is the reaction. Dropping concentration does not require an action (and since action and reaction are similar currency, should not require a reaction) so you need to discuss with your DM whether or not you can (1) by default interrupt any currently declared action/event to stop concentrating at any given time, or (2) if you must wait to stop it when it is your turn.

• For case 2, if as the flying creature approaches you he sees you dropping, would he not adjust his course to try intercept you?


• 
  

  And for case 1, how does the DM determine if he got off that shot before you stopped concentrating? Dex check? Int check? An advocate for that character could argue that they loosed the shot "at the apex" before they you noticed them and chose to stop concentration.

  
  
  

  It might seem to a given DM that you are manipulating the turn system mechanics to provide a mini-time stop that allows you to interrupt their turn. Discuss with your DM. The only mechanical means to an instant response (reaction) seems not to fit this situation.

  
  

Certain special abilities, spells, and situations allow you to take a
special action called a reaction. A reaction is an instant response to
a trigger of some kind, which can occur on your turn or on someone
else’s. (Basic Rules, p. 73)

Since neither of those spells explicitly has that provision, nor does the text on concentration, to interrupt another's turn then this requires a DM ruling in terms of timing.

Arguments for the interruption

Since your concentration can be broken on another character's turn (when damage is done to you) you can reasonably argue that dropping concentration on another's turn is consistent with that, since

You can end concentration at any time (no action required).

Lino's answer is a valid ruling, as would be a ruling that requires that you only act on your turn unless you have a mechanic that allows you to interrupt
another character's turn. Dropping concentration then (only on your turn) would not consume your action - you would still take an action of some sort - but you'd need to wait until your turn to declare that you are dropping concentration.

Whose turn is it anyway?

During a round, each character has a turn.

The game organizes the chaos of combat into a cycle of rounds and turns. A round represents about 6 seconds in the game world. During a round, each participant in a battle takes a turn. The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative. Once everyone has taken a turn, the fight continues to the next round if neither side has defeated the other. (Basic Rules, p. 72)

OK, when it is someone else's turn ... what happens?

Your Turn

On your turn, you can move a distance up to your speed and take one action. You decide whether to move first or take your action first. Your speed—sometimes called your walking speed—is noted on your character sheet. The most common actions you can take are described in the “Actions in Combat” section later in this chapter. Many class features and other abilities provide additional options for your action.

Since the text on concentration does not require an action (small a) to drop concentration, nor a reaction, then parsing that text literally supports Lino's answer: you aren't using an action, so "any time" can be interpreted as "any time, to include when some other character is taking an action within that six second round."

But it's all "happening at once" during a round

A DM can also rule that you only get to declare what you are doing when it is your turn. Interrupting others (even NPCs and monsters) on their turn is not consistent with this being a turn-based game. Waiting for your turn is consistent with D&D 5e being a turn-based game, with the exception - reaction, which this is not required to use - being when you can interrupt another character's turn.

• 
  

  How often will you be happy to see the Monsters interrupt your turn?
  When playing a turn-based game, how often do you want others to
  interrupt you during your turn? And for that matter if, as the flying
  creature approaches you he and sees you dropping, would he not adjust his
  course to try intercept you? It doesn't take an action for him to see your location begin to change, does it?

  
  
  

  Discuss this with your DM and get a ruling. Hopefully, for your idea to work, the GM will see it Lino's way. If not, then wait for your turn and do/declare stuff then.

  
  

"On someone else's turn" is not a time.

The unit of combat time is the round, which is about six seconds.

The turn is not an interval of time. It's a procedure for declaring what a character spends the round doing. If during the round you want to drop concentration on a spell, you can do that, but we resolve it on your turn because you're the one doing it.

You can say, on your turn, "I step back about ten paces, take a shot with my bow, and then stop concentrating on levitate." Or you can do it in any other order, because "at any time". What you can't do is declare a sequence of actions on your turn and then, when you see what someone else is doing, say "Wait, right before she attacks, I wanted to stop concentrating." That would open the door for them to say "Then I want to attack one second earlier, before he stops concentrating."

Initiative order tells us who has to commit to a course of action first.

If you really want to do something at a specific moment relative to someone else's action, you can take a Ready action. Normally, you can only use that to take an action or to move. On the other hand, the rule about dropping concentration says "no action required", not that you can't improvise an action to do it.

However, even if you do Ready an action for "if someone attacks", they get to finish attacking before you interrupt their turn. There are reactions that will preempt the triggering condition (the shield spell, for one) but the Ready action generally doesn't.