The magic number I've often heard is 1,000 hours. But that's highly variable. If your records are clean, and you keep your stylus clean, it could be much more. Some people claim that stylus preservatives (like LAST) can help, too. On the other hand, one mistake in handling a new cartridge, could reduce the number to zero.
The best way to check the stylus condition is with a visual check. Some dealers have a microscope. I've heard that you can use strong magnifiers in home, although I can't remember what to look for.
Sonically, the primary sign are problems with the treble on new records. Also, tracking problems with the cartridge towards the end of the record would be a sign of serious wear.
Age can also have an impact--some have claimed that a cartridge is only good for a year or two--although I'm under the impression that newer cartridges age better than older designs.