Okay, this is a question that i've been dying to ask for ages.

The neck of my guitar is not parallel to the guitar body. If I placed my guitar on a flat surface, the guitar neck and bottom of the body would touch the ground, slightly elevating my guitar so that the top of the body is not touching the ground.

Is that wrong? Is the body and neck of the guitar meant to be parallel?

My guitar is a Les Paul, if that makes any difference.

Cheers guys!
Yeah, that's normal for a Paul. Whether or not you need a truss rod adjustment is another question, but it has nothing to do with the angled neck/headstock on your guitar.

If you have dead spots, buzzing, high action, etc., check out the setup thread.
Ya, adjusting the truss will only adjust the straightness of the neck itself, not the angle of the neck in relation to the guitar. The guitar neck itself could have a bow/curve in it. for example I got a guitar off of my cousin and it hadn't had strings on it for a while so the neck had a bow to it. I had to adjust the truss rod because there was a lot of buzz on certain frets.
Ibanez S520EX EMG 81/85
Ibanez RG350MP
Fender acoustic (Black)

Peavey Vypyr 15
Peavey 6505 212 combo
guitar necks are actually put on at a slight angle and aren't parallel with the body
Guitar Rig:
Fender Telecaster
Martin GPCPA5
Orange Rockerverb 50

Bass Rig:
Squier Vintage Modified Jazz V
Hartke HA3500