Depends on many factors, if your bow hunting and your sure that it's a lethal shot then I'd wait at least 30 min. If your gun hunting and you know that it's also a fatal shot then I will get down immediately. Especially if I see the deer go down.

If the deer runs after the shot (w/gun), sit and listen. Usually, you can hear the erratic running through the woods and sometimes you can hear them go down. When you approach the deer, carefully check to make sure it's dead. Usually the eyes will be open and motionless.