I saw a bunch of questions about this, so I figured that I would post an answer. The best way to kill a deathclaw is by getting up high in an area that they can't get to. The best possibility is climbing up a tall, wide rock. You'll feel cheap for doing it, but I can kill a deathclaw at level 1 using a 9mm pistol using this technique. Just hop up on a tall rock or try to trap them at the bottom of a cliff to pick them off with ease.
Normally, the deathclaws at the Quarry are one of the biggest problems for people (I've never heard of anyone actually going to the deathclaw cave). One of the best ways to kill them is to go up on the huge tower and rain down sniper fire while the confused deathclaws try to get up to you. If you can't snipe them out, you could also get the CZ57 Avenger or another minigun and kill them pretty quickly.
If there is no rock or you are not around the quarry, you could go to the area NW of New Vegas and get the Alien Blaster or YCS (depending on whether or not you have the wild wastelander perk). If there are only a few deathclaws around, try to shoot the toughest one with a sneak attack and back up while your companions try to take them down. While they are getting hit, try to kill all of the deathclaws.
Runite posted... Max charge YCS round to the face from stealth. Or, GRX/Turbo circle-strafe with a melee weapon and Super Slam.
Funny you should mention the quarry, though; some of the most fun I ever have with energy weapons is insta-killing the Mother Deathclaw with a chain reaction of Meltdown-detonated Deathclaw Babies.
i know what you mean. camping out in the quarry and just figuring out all of the different cool ways to handle the DCs is tons of fun. i really enjoy explosives. --- Slaughter is the best medicine. http://img194.imageshack.us/img194/7944/argylegargoyle.jpg - artwork by masterpug53
The AI is onto the elevation trick this time around, try again. Enemies without long range capability will run away from you if they can't attack you.
The way to get around it is to use their inability to fall like any distance at all. So you backpedal up a hill while firing or recharging AP and when the Deathclaw gets close you jump off a small ledge. Then you get free shots while it has to go around and then find another ledge and start all over again.
In the Quarry there's a conveyor belt thing you can run up and jump off over and over again to buy yourself space while you shoot the Deathclaws. It's way easier than camping on the crane and trying to hit all the Deathclaws at extreme long range while they're running around. --- Mind the gap.