OK, there are several things to keep in mind when looking at disease transmission in history.

First, Europeans were not uniquely disease-ridden. The Old World in general had a harsher disease climate than the New World.

Europeans had plenty of diseases, but many of the great epidemics in history, including the plague of Justinian (6th century) and the Black Death (14th century) originated in Asia and spread out from there. Africa also had a terrible disease climate, partly due to mosquito-borne diseases like malaria and yellow fever. When Europeans went to Africa, they were actually much more likely to die of fevers than to give any European disease to the people who lived there. The short version is this: any group of people who participated in trade, whether European, Asian, or African, was guaranteed to spread disease around.

Globally speaking, there are certain factors that tend to lead to more disease.

Where you have large populations and cities, you have more disease. There are a couple of reasons for this. First, if I have measles in a big city, I can spread it to more people than if I live on an isolated farmstead. Second, premodern cities were filthy! Where you have cities, you have improper disposal of human and animal waste, which can contaminate water supplies. Third, where you have close contact between humans and animals, you have more disease. You can see this both in terms of diseases like cowpox and bird or swine flu, but also in terms of a disease like the plague: carried by rats and spread to humans through fleas.

A second misconception has to do with the idea that Europeans were somehow immune to the diseases that they carried, perhaps through some kind of gradually acquired immunity passed down through the generations. But the fact that a population has had a disease for a long time doesn't guarantee that it has become immune to it. Diseases vary a lot in terms of how (or whether) immunity can be acquired.

The best example of this is smallpox. Europeans had had smallpox for a very long time, and yet every European was born entirely susceptible to smallpox. It didn't matter if both of your parents and all of your grandparents and great-grandparents had had it; you were still born fully susceptible.

The somewhat unusual thing about smallpox is this: it kills a lot of people, but all survivors are permanently immune. (Obviously, not all diseases work like this, but smallpox does.) So, you wind up with two possible disease scenarios when smallpox shows up in an area:

Scenario One: Smallpox spreads to someplace where smallpox shows up regularly. Let us imagine that we are looking at a town in England where smallpox has typically shown up about every ten or fifteen years. If smallpox hits this town in 1600, many of the adults who live there will be safe. This isn't because they inherited immunity, but because they survived the disease when it hit in 1590, or 1578, or 1564. But when the disease strikes in 1600, every child born after 1590 will be susceptible, and many of them (perhaps 30% of them!) will die from it.

There are also social factors involved. Smallpox is a horrific disease, no matter how you look at it. In 1600, there were no vaccines (not even variolation) and no effective medicines against it. The best thing you could do for a smallpox patient was keep them warm and provide elementary nursing care -- cleaning them and making sure they had food and water. Even with that care, lots of them would die from the disease. But at least they would have had a chance -- they didn't die of thirst or cold.

Scenario Two: Smallpox spreads someplace where smallpox hasn't been seen in generations, or where it has never been seen before. (Imagine a town in the New World.) When smallpox arrives, it spreads very rapidly, and it is incredibly debilitating. No one has lived through smallpox before and become immune, and so virtually everyone in the community falls sick at once. No one is well enough to care for the sick, and tons of people die. The deaths include all of the people who would have died of smallpox under any circumstances, but also includes people who might have survived had someone been well enough to bring them a blanket and give them broth to drink.

There are also long-term effects to consider when speaking of the New World. Imagine that this population, weakened by smallpox, wasn't able to do enough planting, or hunting or gathering in the following season. Malnutrition could follow. Imagine that another new disease shows up the following winter (measles, or influenza, for example) and strikes the already weakened population. Imagine that Europeans are eyeing the land and thinking about expanding. This Native American population will be less able to resist than if their population was larger and healthier.

A third misconception is that Native Americans lived in a disease-free paradise before contact. Native Americans do seem to have had fewer major epidemic diseases than Europeans, but wherever you have people, you will have diseases. When you look for Native American diseases, you find the same patterns that you find in the Old World: where you have larger populations (as in cities like Teotihuacan) you find more disease than in areas with smaller populations. But early European explorers were always talking about people getting sick when they came to America (usually using very vague and unhelpful terms, like "fevers.") They even had a special term to describe the fact that Europeans who came to America often got sick, and some of them died. They called it "seasoning." Significant diseases that originated in the New World include Chagas' disease and leishmaniasis. Syphilis probably did, too, although there is a big debate on that.

It is true that massive epidemics of new diseases struck Native Americans after contact, and those epidemics had devastating results. But the often-told story that contrasts "immune Europeans" and "susceptible Indians" is just not correct.