Not everyone particularly likes him, but Jared Diamond's "Guns, Germs and Steel" explores pretty much this exact question (as part of a suite of "why did Europeans conquer the Americas instead of the other way around" issues). Glossing over a lot of the details and specifics, the argument he makes is that various factors -- geography, indigenous flora/fauna, etc. -- allowed densely-packed settled human populations to develop in Europe/Africa/Asia before the Americas. And such densely-packed populations are far more conducive to the development of epidemic diseases, which would be why diseases brought by Europeans wrought such havoc on the Americas but not vice-versa (except possibly for syphilis, but that one's still being debated).

Among other things he says that there were no (or almost no) animals suitable for domestication and mass herding in the Americas. Therefore the native Americans had no contact with herds of animals that would have bred diseases of that kind. Most of those epidemic diseases that killed off lots of people apparently stem from chicken and pigs. (note: guess why it is called "swine flu").

Also, the spread of disease did go both ways. Syphilis came from America to Europe.

It's also worth noting that Europeans are not at the top of the food chain in terms of disease resistance. Various European powers raised a flag on New Guinea, but they never successfully colonized it. It's a cesspool of disease, and Europeans never managed to do more than establish a few trading posts on the beach.

Because the Americas were isolated while Europe had engaged in extensive trade with the middle east, asia, and africa for centuries. European resistance to disease did not come free, it came at the cost of having lived through several catastrophic pandemics. The black plague (among other endemic diseases such as smallpox, measles, cholera, and malaria) killed hundreds of millions of Europeans, the Europeans of the 15th century were the descendants of the survivors of past outbreaks.

I'm guessing that a lot of the European explorers did die from disease, but if 75 out of 200 Conquistadors died from Cholera, Amoebic dysentary, Yellow Fever, etc... It probably had much lesser impact on them than 300,000 out of 100,000 people in an Aztec or Inca city dying from Small Pox.

To add to what has been said, the article notes that the Europeans responded well to infectious diseases- they quarantined and evacuated. This limited the spread and the overall lethality of any diseases on the Europeans.

But also the filthiness of Europeans protected them. Their filthiness had been developed over millenia as the population became more dense, giving lots of time for the population to evolve immunities (and for the diseases to become more potent).

This arms race meant that the diseases were tough, the Euros were tough, but those races who had been spared the arms-race of filthiness were sitting ducks to the Euro super diseases.

I've no facts but will speculate.

It could be that Euro-african civilisations were more effective at cultivating new diseases thanks to the crossover between animals and humans.

http://en.wikipedia.org/wiki/Domestic_animals

Guinea pigs and llamas seem to be it for the new world. Whereas the Europeans had a vast list of animals available. They'd live in tight confines with pigs and chickens and cows during long cold winters - fabulous creatures and circumstances for cultivating new strains of disease.