Here's a trick I got from America's Test Kitchen on PBS:
Take one slice of white bread for about each 1 1/2 lbs. of beef. Remove the crusts and dice the remaining bread. Add enough milk to make a panade (thick paste). Add A-1 or Worcestershire and spices. I usually use garlic and pepper, maybe curry if I want a little kick. Mix the panade thoroughly with the ground beef. The panade acts as a binder to replace some of the fat that drips out, and the A-1 or Worcestershire replaces some of the flavor lost with the fat. You can grill these to a nice thick crust, and they'll still be very moist inside.
Edit: I see someone else already mentioned this. Doh! I didn't read the whole thread...