I always hear the stories of how the Europeans brought sicknesses that wiped out entire regions of Natives, but rarely hear of any other Human->Human sicknesses that the Natives spread (if there were any). I do realize that swamps and malaria and whatnot were a big deal, but never you never hear too much about human spread sicknesses in the early America's
Europeans grew up with diseases like smallpox because a lot of them lived with or near livestock. Living around livestock means it's more likely to have a disease jump from, lets say a pig, to a human. Hence why we have swine flu or bird flu. Native Americans didn't really have many domesticated animals (llamas and the their relations non-withstanding) meaning they didn't get exposed to so many diseases. So when they got smallpox infested blankets (intentional or not) from Europeans, the Europeans had an immune response and antibodies to protect them, whereas this was a brand new disease to the Native Americans. Their immune system just had no clue what to do.
As for what diseases Europeans got from the Americas, Syphilis is the one that comes to mind. It was in the Americas before Columbus reached there, and it is believed that his sailors carried it back on their return voyages.
You may want to check out some questions in the FAQ. In particular, I think this question and this other question ought to provide some good info for you.