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From my experience, whenever I melee an opponent who doesn't have any shields, the melee always kills them. If you melee when they still have shields, then only their shields are removed (thus taking a max of two melee attacks to kill an opponent).

Edit: The Bungie Weekly Update for September 24 has more information about how melee attacks and headshots work in Halo Reach. The basic idea is the same: melee will destroy any remaining shields (and nothing else), while a melee to a shieldless opponent will kill him.

The answer appears to be 15 to 20 "face shots" with the DMR. I'm not sure if that's what just magically ends up being enough to get a head shot at distance, or whether they really start losing HP. The shots were basically directly to the face, they will bring up their shield immediately after (so don't just hammer on the trigger), and then drop it again and you can take the shot again. Just keep doing it until they fall over.