To give an example from a somewhat recent game, the party was fighting two mages who had cast greater invisibility on themselves. The fight took place in a cellar, and the mages didn't need to Hide every turn, allowing them to cast fireball and cone of cold instead. They were effectively hidden until they cast a spell, at which point the characters would see and hear the point of origin and surmise the mages' general location. Also, when the mages moved, they rolled Stealth checks, with a failure indicating that the player sensed their movement and knew their general whereabouts. This meant that melee players were blundering around the room, swinging at empty squares, desperately trying to hit something.
None of this is by the rules, of course, but it was a lot of fun.