Blackened or charred meat is usually the cause of concern for grilled foods when they are linked to cancer. There is no clear evidence, but cooking meat at the high temperatures you use to grill—as well as broil and fry—creates heterocyclic amines (HCAs) and polycyclic aromatic hydrocarbons (PAHs), compounds linked with some cancers.
The general consensus that I have read about says that the risk is quite low as compared to other risk factors like being overweight by 30 lbs, or not exercising. If you are generally concerned though, you can take measures to help reduce the chances, for example, grill fish and vegetables, trim the excess fat to prevent drips onto the coals and flare ups. Probably most importantly eat a variety of fruits and vegetables especially cruciferious veggies, like broccoli, cauliflower, cabbage etc...they help remove these compounds quickly from your body and reduce your risk.
If you still prefer meats and poultry like I do, there is hope. Flavor meats with marinades and rubs. Research in the Journal of Agriculture and Food Chemistry showed that marinating red meat in beer or wine for two hours significantly reduced HCAs. Scientists believe the antioxidants in these marinades block HCAs from forming. Kansas State University study found that rubbing rosemary, an herb known for its high level of antioxidants, onto meats before grilling cut HCA levels by up to 100 percent. Herbs including basil, mint, sage and oregano may have similar effects.
I wouldn't give up grilled food for the world. I hope this helps. :) I say enjoy it.