When making hamburgers, I prefer to grill the beef until it is very dark and the outside is entirely black. I know that it is dangerous to eat beef that not cooked enough, but is there any hazard in eating beef which is cooked too much?
From a food safety point of view, no. There is no danger, because the meat contains no pathogens after overcooking.
From a "healthy living" point of view, it might be a problem, because you can have created carcinogens by charring. But we don't discuss such topics here, because nobody in the world knows how much eating charred meat contributes to the risk of developing cancer.
From a cook's point of view, you are doing it wrong. Well cooked meat is juicy and tasty. Overcooked meat is tough as shoe leather. You can continue doing it, if you want to, it is just irrational, like saying "I let my salad wilt for at least a week before eating it, I prefer it that way."
There are several studies linking foods cooked at high temperatures, and especially charred foods, to an increased risk of cancer. So far these studies have only been conducted on animals, so there is no conclusive proof that it has the same effect on humans, but as humans are animals, it would seem at least possible.
The National Cancer Institute has a good summary, here.
On a different note, why?