Most Likely: Contamination is more likely with ground beef than it is with full cuts. However, getting sick from a burger is still fairly uncommon. According to the Centers for Disease Control and Prevention, there were only 90 reported cases of people eating contaminated hamburgers in the United States in 2001 (though many more may have gone unreported). Forty-six of those 90 were hospitalized.
Worst Case: For most healthy adults, the worst that's likely to result from eating a rare hamburger is food poisoning. At its most severe, this would result in several days in bed with a stomach illness. The U.S. Department of Agriculture recommends that you never eat a rare burger (cooked to less than 160 degree F), since bacteria may survive in it. This is particularly important for the very young, the very old, the immunosuppressed, and pregnant women, who are all more susceptible.
So I guess the moral of the story is to at least cook your burger to medium. Otherwise you may end up with some food poisoning. Besides, unless you are a vampire needing a little extra blood, who wants a bloody burger?