I often hear about the devastating effects of smallpox and other diseases on native peoples due, in large part, to the fact that the diseases were brand new to the previously isolated (from Europe/Asia) people of America and Australia. Logically, the same lack of immunity to diseases of the natives could impact the Europeans. Did they?
I think part of the imbalance in disease exchange lies in the fact that Europeans kept more animals in close contact than Native Americans did. There's some evidence that syphilis spread from the New World to the Old, but not enough to be definitive. It might have just been poorly documented. I think Jared Diamond's Guns, Germs and Steel explores this pretty thoroughly. Here's the wikipedia article on syphilis