Answer:
As a general rule of thumb, you should never eat raw beef as there is a small chance of the beef being contaminated with E. coli O157:H7. In addition, raw beef can carry other bacteria such as Salmonella, Clostridium, Camplyobacter, etc, as well as some parasites and viruses.
However, there are many stories out there about eating raw ground beef and eating raw meats in general. You can eat meat raw, but you should be aware of the potential risks involved in doing so. No source of meat is 100% safe - cooking reduces the risk of illness and death significantly.