A single 00 Buck Pellet (33 Caliber) is capable of cleanly killing any deer on broadshots out to 100 yds. IF it hits the heart/lungs. The problem is that with a shotgun you aren't placing shots like you do with a rifle. Pattern density is the key. Extra full chokes will help extend your range.

I'd say the farthest that you can shoot is at the distance in which you can no longer put one pellet on a pie plate 100% of the time.

I've had great success with the Winchester SuperX 3" 00Buck.