When Europeans came to the Americas, they brought with them "Old World diseases" that decimated the Native American population. There's a big list of them here. Were there any "New World" diseases that affected the colonists?
The only ones I have ever seen were referenced in the Columbian Exchange as being passed to the Old World:
- bejel or nonvenereal syphilis
- Chagas disease which is more of a parasite from Central/South America
- pinta which is similar to bejel and another form of syphilis
Mostly the effects, if you believe Jared Diamond, came more from the crowded conditions of the European cities where many of the ships that came to the New World left from.
Some places that mention these: History Now - Columbian Exchange
European explorers encountered distinctively American illnesses such as Chagas Disease, but these did not have much effect on Old World populations. Venereal syphilis has also been called American, but that accusation is far from proven.
Of course you also have the discussion as to whether or not Syphilis came from the New World with Columbus' return, Did Syphilis come from the New World?
Viewpoint: Yes, syphilis originated in the New World and was brought to Europe by Christopher Columbus's crew.
Viewpoint: No, syphilis was a disease that had long been in the Old World; it was simply a coincidence that it flared up shortly after Columbus's return from the New World.
I also found this repeat on some of the other information that backs up what was said before: New World Infections
There were infections in the New World before 1492 that were not present in the Old (Chargas' disease, for instance). There were those it shared with the Old World, certainly one or more of the treponematoses (a category including syphilis) and possibly tuberculosis; but the list is short, very short. When we list the infections brought to the New World from the Old, however, we find most of humanity's worst afflictions, among them smallpox, malaria, yellow fever, measles, cholera, typhoid, and bubonic plague.
There is more here from Alfred Crosby on his book on The Columbian Exchange - worldwide impact of the New World
One of the main topics mentioned in Jared Diamond's Guns, Germs and Steel is that communicable diseases such as the Old World diseases (plague, smallpox, typhus, cholera and measles in particular) generally made their way to humans from close contact to domesticated animals (cattle mainly, but also pets and vermin).
Almost all the large mammals of the Americas died out after the last Ice Age (which is part of why most American civilisations were hunter-gatherers and none were as successful as the Eurasian societies that conquered them — it's worth reading the book if you want to know more about this, as I'm oversimplifying), so very few animals (llamas, alpacas and turkeys being notable exceptions) were domesticated in the Americas, so very few diseases evolved to infect Native Americans before 1492. A substantially lower population density in the Americas also meant that diseases were more likely to burn themselves out, as they had a smaller pool of potential infectees.
Very few diseases are thought to have moved in the other direction. Of these, the most notable is syphilis and, as MichaelF mentioned in his answer, the continent of origin of syphilis is still the subject of much debate.