If you have read the HowStuffWorks article How Cancer Works, then you know that there are many different things that can cause cancer. You would think that cooking meat over an open flame would not be one of those things, given that people have been cooking meat this way going all the way back to the caveman days. Unfortunately, it does appear that grilling, broiling or frying meat produces substances that have a connection to cancer.
Heat has a general property of allowing chemicals to change from one form to another. You see this happen whenever you cook an egg -- the heat changes the proteins in the egg and solidifies them. In the case of meat, high temperatures convert things like fat in the meat into substances called polycyclic aromatic hydrocarbons. Polycyclic aromatic hydrocarbons are groups of benzene rings, and, like benzene itself, these rings can be modified in the body to produce chemicals that damage DNA. According to Encyclopedia Britannica:
How much of a risk does well-done meat present? According to this article, "For the age groups that we're studying, the rate at which women who eat well-done meat are developing breast cancer is nearly five times greater than the rate among women who are not cooking their meat well-done." So it seems that there is a noticeable difference.
If you want to avoid these risks entirely, boiling meat is a good way to prepare it...