In my games, I go with the convention that most creatures just die when they go below 1 hp. So, most of the time, when the monsters or NPCs reduce a PC's hit points to 0 or less, they don't expect him to get up. If one of the other PCs manages to get the dying character up, the typical reaction will be to prioritize that that character as a target to prevent him from doing it again rather than to CGD dying characters. If a dying PC rolls 20+ on his death save and gets up by himself, his opponent
might hit him again when he's down "just to make sure he stays dead", but he could just as easily shrug it off as a fluke and pay no special attention the next time he goes down.
The above only applies to dying PCs, though. Sleeping, held or otherwise helpless PCs are fair game for CDGs.
That said, I recently reviewed the rules of CDG in 4e, and it turns out (surprise, surprise) that they are slighly different from, and in some ways, less deadly than, 3e:
1. A CDG is not an automatic hit. A helpless target gets -5 to all defences and is prone, which grants combat advantage to adjacent melee attacks, but the attacker could still roll low. If the attacker had a 50% chance to hit previously, he still has a 15% chance of missing, or a 25% chance if he is not using a melee attack.
2. A CDG automatically kills only if you deal damage equal to half the target's bloodied value (although getting hit for extra damage when you're already dying is never a good thing). Otherwise, a CDG is "just" a critical hit and deals maximum damage for the attack (plus other bonuses for a critical hit). Thus, CDGs are only really dangerous with encounter and recharge abilities, or if your opponent has a seriously damaging critical attack. At least for the PCs, they will not always be facing enemies with high crit, vicious or vorpal weapons.
3. You can't CDG if you are not adjacent, so you must be right next to the target even if you have reach. This is not always possible or advisable, especially for artillery or controller type opponents.