I've heard a lot of them, and almost exclusively from people who hate cats or animals in general, and have a problem with anyone having one. There's a lot of classics; how cats scratch and destroy everything, how they leave their hair everywhere, they never get attached to humans they get attached to places, they have to live outside otherwise they're 'unhappy', etc.
I've heard some strange ones too. Some people say that if you swallow a few cat hairs, you die. I've heard once that if you swallow a cat hair it can pierce through your kidney. Another really strange thing I've heard is that you shouldn't let a cat near a baby, because the soft spot on their heads smells nice to cats and they will eat it (?!?).
I'm not really sure if people really believe these things, or if they just make them up to scare potential cat owners. Both ideas are a bit disturbing for me.