In the movies big fights tend to rage all over. The area the fight takes place in is changed by the fight. The brawl is almost always as destructive to the environment as it is to those fighting in it. In RPGs this is less the case. Whether due to being snapped to a grid or just because of the mechanical intensity a lot of groups have combats that leave the area the fight takes place in almost pristine. Heck, in some systems you could probably run small skirmishes (say 10 on 10 fights) in a china shop and not damage a single thing on the shelf unless someone deliberately started pushing them over. Today, I want to talk about that.
As The GM, It Falls On You
To make things clear, this is one of the areas of a game that falls on the GM and the GM alone. The Players, in most games, literally do not have the mechanical clout to rule one way or another on these things. Furthermore, as they are world things, and the world is in the purview of the GM, it is thus the GMs business to handle it.
This isn't to say that a player can't make suggestions. Nor that a GM can't listen to them. However, if you want collateral damage and things like it to be in your game, you need the GM to be on board for it. That out of the way, how does it work?
Keep In Mind What Is Really Going On
The trick to having incidental and collateral damage in your fights is to keep in mind what is really going on. Not mechanically, but if it were real life. Combats are violent things full of chaos and life. Unless you are playing GURPS with its 1 second round timers - and even in that - so much more is happening in a combat round than what mechanically happens. An attack can be one big, powerful swing or multiple smaller ones. Even a character that makes no movement action is probably stepping around in a broad circle with their opponent as they circle for advantage. Arrows that miss their targets have to go somewhere. Swings that miss are also likely to do something.
A character who hacks an opponent to death with an axe is likely to get covered in blood from the wounds they have inflicted. A character wearing a cloak, or other loose clothing, will likely find holes in their garments after a big fight even if none of their blood was drawn. Long hair can become unbound. Items can be dropped. People will fall in the mud. It's combat. Just remember that.
Why Does This Matter
Why waste a post on this? I mean, who cares if someone is covered in blood after a fight or not? Well, this matters for a couple of reasons, both of which can enrich your game.
The first is that it helps to bring your world to life. You can use details to add spice and danger to the feeling of combat, even those that are close one. A near miss attack can instead slice clothing open, or cut hair loose. By mentioning it you let the player know how close it came, you also paint a more vivid picture of the fight, and combined it makes the world more alive.
The second is that being covered in blood or having tattered clothing is a consequence that deepens the ramifications of combat. I can't say how many D&D groups I've seen murder a group of bandits or something on the road, then just walk into town to go shopping and get an inn room. Ultimately, this is fine, but think about it: you have a group of travelers who are heavily armored and armed, covered in blood, and looking to shop/get a room like nothing is going on.
With number two, if that isn't a layer you want on your game that is fine. However, for some games it can be a lot of fun to add things. It also helps the players remember to do things like take baths, buy new clothes, and keep themselves sociable when they want to make a good impression. Of course, your mileage may vary.
What To Break?
Almost anything around can be broken, and perhaps should be fair game.
On characters you can cut hair, clothing, mark gear, or even knock things free. Be careful not to damage/break something beyond use, or to where the character could lose things with value - unless you have permission for it or it is from a successful attack - but still have fun with it. Don't be afraid to play up the descriptions either, or to throw players around or down in the mud - without requiring the player to stand up as if they had suffered a knock down. In doing so you add not only better description but also dynamism to the fight, which makes it feel a lot less static.
In the environment almost everything is fair game. Candles can be knocked over, tables can be broken, chairs can be flipped, and walls can be hacked. Endangering objects can also be a good way to get the PCs to spend actions on non-attacks as they act to protect precious things (think most Jackie chan movies when he's in a shop of some sort.)
In the end the more fun you have with it, the more fun your players will. And isn't fun the point?