What size hole should be drilled for wire that will be pulled through the walls?

3/4 in hole good, 1 in hole better. That gets you a full 1 and a half inches from nails and dry wall screws etc and allows electricians to come back and pull more wire etc. Depending on circumstance you may also want to put steel plates over the 2x4 where you drilled the hole, so if some idiot comes behind you with trim nails longer than 2 inches you wont get a short or set the house on fire also a good idea where plumbers drill for pipes... Irecommend a short auger bit to drill with and angle headed Drill. Milwaukee makes an Excellent one. I work as a remodel carpenter and am a journeyman electrician.