This term was brought up in another question. I know that players can receive signing bonuses etc. But can they receive performance bonuses in a salary capped league? To my knowledge, in the NHL for example, any money given to a player other than his regular salary is not allowed because it is a way to get around the NHL's salary cap. With that being said, how are performance bonuses handed out and in which sports?
Bonuses in the NHL are completely legal, but only as a part of a player's contract that affects his cap hit.
Many ELCs (Entry Level Contracts) for high profile rookies include performance bonuses. As per the (now expired) CBA, the maximum rookie salary during an ELC is $925,000. However, as much as $2,850,000 can be added in bonuses, which raises the cap hit of such a contract to up to $3,775,000 if it also includes a signing bonus. See this example.
There are two different kinds of bonuses: signing and performance.
Signing bonuses are pretty straightforward. Either the money is paid right when the contract is signed, or there are bonuses at certain times of the year (I have heard of a player getting a "signing bonus" in the middle of his contract at the season's start that was unrelated to performance).
Signing bonuses have been particularly popular in the NHL this year due to the labour situation. The current CBA expired on Saturday night, and as the players are now locked out and will not receive any of their regular salary, a lot of players who signed in the summer recieved larger signing bonuses than normal (which they would be paid immediately, before the CBA expired) due to the labour situation.
Performance bonuses (in the NHL at least) are also fairly straightforward. I've heard of bonuses for goal total, assist total, team points, making the playoffs, and I'd imagine there are many more. Unfortunately the exact details don't tend to be made public.
If you're interested in knowing more about the salary cap in the NHL, I'd definitely recommend visiting general fanager. It's a great resource for all the information you'd ever want to know in regards to the salary cap. As of right now, it's only for hockey, but I believe an NFL site is being developed (not sure exactly where they are with it).
Update for the 2013 CBA
Performance bonuses are perfectly legal in the NHL CBA, and they count against the cap. Teams are allowed to exceed the cap by 7.5% as a result of performance bonuses (but not more than that), though of course they have expectations of whether a player is likely or unlikely to meet a goal and plan thereon.
Further, only certain players are allowed to be given performance bonuses. According to capfriendly:
These are players who the bonuses make the most sense for - players where you might want to give a contract to that is low in guarantee but allows them to make more if they do well.