I've installed 20A switches on 15A circuits before, namely on the circuit supplying my kitchen lights. It was primarily to take advantage of the side-clamp wiring available on these beefier switches instead of the curl-and-screw flavor of side-wiring, or the push-in wiring, that you normally see on 15A S/P switches.
A friend of mine says that having a switch of higher capacity than the branch circuit breaker can cause the breaker to trip. I say he's full of it; a switch is a switch, and a 20A S/P will just be beefier than a 15A. As long as it's rated for at least the amperage draw of the circuit, you're fine, IMO.
On a related note, does the same apply to outlets? He may be confusing using a 20A switch and using a 20A outlet; the outlet, unlike the switch, supports plugging in appliances that will draw >15A, and if you do, that WILL trip the breaker (though as 20A outlets support plugging in parallel-bladed 15A appliances, if you KNOW the branch is 15A and don't try to plug in a T-bladed plug, you're still OK).