Please no flames from the vegetarians.
Disregarding the taste effects (I personally prefer medium to rare), there are two good reasons to cook meat to well-done. One, when animals are slaughtered, the method does not always result in a sterile end product. Thus, bacteria from the animals intestines can spill and contaminate the meat. Such bacteria include E. coli 0157, campylobacter jejuni, salmonella and shigella. Two, eating the undercooked meat of animals can lead to taeniasis. If you eat infected raw beef, you can get Taenia saginata, and raw pork leads to Taenia solium. In the US this is not common because meat (for the most part) is inspected, but much more common worldwide.
A more severe form of pork tapeworm is called neurocystercercosis, which occurs when you eat the eggs from human feces. Thus the classic infectious diseases board exam… How did the Hassidic Jew get neurocystercercosis (since he doesn’t eat pork)? From eating food contaminated with someone else’s feces.