What the title says. Is this something that's allowed in your games? Does your group have specific rules that've made for something like this? etc.

As far as I'm aware, there isn't anything in the basic rules for this, though I could very well be wrong in which I would also be very interested in that. 

Edit: These are all really great answers that touch on the blind spots I had when asking about this.

And with everything that's already been said, I would like to ask about a more specific scenario. Say you're hunting for a dragon. You know that it's dangerous, so you want to prepare thoroughly. There's also a town nearby, so you absolutely don't want the dragon to fly away and go burn it down in retribution. You could use spells, by spells can fail or be broken through. So you set up a trap. You put down a bait, and prepare... something. Let's say a huge ballista, that you've somehow managed to get into position for the sake of the hypothetical. The dragon swoops down, you fire, and if you manage to hit, the bolt (which for sake of argument is specifically prepared to do this) tears through the webbing of the dragon's wing. The dragon remains largely otherwise uninjured, but is rendered incapable of flight. All of this happens with a lot of planning and (most importantly) fully outside the constraints of normal combat.

I basically just want to know if it's really even worth suggesting something like this during games, or if the general consensus is that it'll just unnecessarily muddle things up or something of the like.

Quote from SulivannVance >>

What the title says. Is this something that's allowed in your games? Does your group have specific rules that've made for something like this? etc.

As far as I'm aware, there isn't anything in the basic rules for this, though I could very well be wrong in which I would also be very interested in that. 

 Targeted attacks on monsters is not something that is part of 5e mechanics. If it was, combat would be radically different. Next up, targeting eyes for blindness, etc etc etc.

To paraphrase an extremely long copypasta (which you can find in my post history): You wanna hit just the wings? So you definitely don't want to hit the head or the heart?

There are no Rules as Written for targeted attacks in 5e. My group doesn't have any homebrew rules for it either because anything the players can do the NPCs can also do. Do my players want enemy creatures to target their legs to cut them off and stop them from moving? No they don't. 

If the players want to stop something from flying they can use Earthbind. That's what the spell is for. 

As a DM, I always am willing to try new house rules with the caveat that the creatures they face can do the same thing. My players are not too keen on losing their sword and their arm in the same attack so things like this tend to be avoided.

The only time I have such things happen is under a set of house rules for "extreme damage". 

Basically, you cannot target a creature's wings or limbs or neck or head. However, if a creature (including PCs) suffers in a single attack (not a round, one attack) damage equal to one quarter its total hit points, "something happens" that severely impacts it.

The something is always narrative (OMG kat, you cut it's arm off!) (holy cow, Hector, you were just scalped!). A creature with wings is likely to be affected in such a manner.

Otherwise, nah. Remember that anything that can happen to monsters can happen to PCs. That is a core foundation of the game.

Closest you get rules wise is the DMG optional rules for Lingering Damage or the Massive Damage rules: https://www.dndbeyond.com/sources/dmg/dungeon-masters-workshop#Injuries

I dislike allowing called shots: such rules are rarely ever capable of being balanced.  If you want to flavor it, that's functionally what you're doing with the Great Weapon Fighting and Sharpshooter feats- taking a penalty on the attack roll for a big bonus to damage if you do hit.  I don't think further rules for crippling an opponent's limbs would be a good thing for the game.

One of the issues is that the way 5e is set up, called shots don't fit naturally into the set up and remain balanced.

In STA, you can have called shots. However, it increases the Difficulty of the shot by +1 (which is the game's natural way of handling modifying difficulty on-the-fly), and the way the game works, unless you're relying on a Hail Mary, you have to commit some of your spendable resources, so it's a bonus that requires paying for. You don't do called shots unless you feel there's a specific advantage to do so because it makes it more likely to miss and it costs you to even try.

5e struggles on both of those accounts. The natural on-the-fly method for changing difficulty is Advantage/Disadvantage, but because it doesn't stack (unlike Difficulty in STA), then the mechanical effect quickly loses impact. You could start messing around with AC, but that's problematic as well. With Bounded Accuracy, a +3AC is going to be more an issue fighting a 25AC Tarrasque than a Goblin, even though you'd expect it to be much easier to hit the leg of a Tarrasque than a Goblin. There's a reason why the game is reluctant to let you stack bonuses to AC. It's doable, sure, but the game doesn't like it and if it is allowed to be done with less restraint, it causes issues.

Maybe you could instead allow a Dex Save for the target. That doesn't explain how the Barbarian managed to hit the Tarrasque's eyes...but it makes some sense. The extra roll does double down on one of 5e's weakest points - round times - and breaks one of it's mentalities of only having one d20 roll for each attack. It's even further from the normal methods of adjudicating attacks. Lastly, balancing the disadvantage of having to pass two checks with the bonus rewards would be doable, but not easy.

The final method I can think of is giving Martials a Battle Manoeuvre type of system. That would be treading on the toes of the Battle Master subclass, though. It's the most likely candidate for it though.

Honestly though? I think the whole d20 system would need to be rethought from the ground up if we wanted called shots to be a natural part. Ideally, I think you'd want to scrap it completely and rebuild the system with things like that in mind. Then you run into the dilemma of whether it really is D&D you're playing anymore, and not just another game entirely.

Called shots tend, as others have said, to make the whole thing unbalanced. I will occasionally (very rarely) allow a called shot, but the general rule is it has to be something you've worked for (such as flying up to the head of a monster to try and hit it's eyes), and it will only do something on a critical hit. My general rule is that the effect is thematic and narrative, and I try to make it change the combat without changign the difficulty. For example, in my last session a character flew up to the head of a giant boar and tried to slash its eyes. Had she rolled a crit, I would have made the beast, which had been shaking to try and dislodge the party climbing it as legendary actions, immediately rear and stomp (bad for everyone under it and on it, IE the rest of the party) and become blinded in that eye. It then would have been enraged, gaining an additional legendary action.

So far as Called Shots are concerned though, I mainly allow it after the attack kills a foe, IE "How do you want to do this".

To be honest, if your players manage to injure or break a creature's wings so severely that they can't fly, they're either already dead or have a huge injury that should also effect them in a number of others way in the combat, such as rapid blood loss.

If you want to make things logical here, you would have to make a lot of custom rules to fix aspects of the game that are even more confusing and unrealistic than before. With the other option of saying "Too bad, this is the only house rule on this subject" risking upsetting players.

Another option would just be to redesign monsters. A flying dragon, instead of having like, 100 HP flat, could have four 25 HP chunks to reflect its four major powers of flight, fire breath, fear, and bigness. Dealing 25 damage to one of these aspects is required to overcome that aspect. You can attack its bigness by making attacks while climbing it, getting big yourself, or otherwise attempting to counteract the narrative problem that this beast is just too big to properly fight. If you can't overcome that problem then you can't kill a dragon by just stabbing it in the toes a lot.

Food for thought.

Quote from BoringBard >>

To be honest, if your players manage to injure or break a creature's wings so severely that they can't fly, they're either already dead or have a huge injury that should also effect them in a number of others way in the combat, such as rapid blood loss. 

This right here. Remember, HP is an abstract concept. If the creature has 100 hit points, all but the last attack might be dodged with the lost hit points representing the target tiring until it can no longer avoid the final blow.

For something like a big cinematic dragon fight, I do those in stages. So the first stage might be on the ground because it's not taking the fight seriously, second stage has it flying around and breathing, and third stage has it back on the ground, angry and frantic.

If you want to allow targeted attacks on the monsters then the monsters need to be allowed to have targeted attacks on the players.  If you want to allow a monster to be crippled from flying then shouldn't the monster be able to retaliate and take out the fighters knee so he has half movement now?