Apparently, Batman Arkham Asylym had a "bug" in the cracked version - Batman could jump just a little bit less or something, which meant there are places you can't reach, which makes the game unbeatable. Or so I've heard it advertised - I think an actual properly cracked version suffered no problems.
There was Red Alert 2, too (and also Generals, if I remember correctly) - if you start an illegal copy, you can play but in about a minute after the game start, all your buildings blow up and all your units die. Which is cool in theory but in practice it was just annoying - it meant any time I'd reinstall my OS I had to remember to reinstall RA2, otherwise if I played a game, I'd realise I had to install it again, and I'd need to wait for 5-10 minutes wasting time. Also, again, a properly cracked game actually has no problems.