I'm looking at another Les Paul. The price on it is really good. It's almost too good, which makes me suspicious.

Is there any way to check to find out if it's stolen? I'd hate to shell out $$$ only to have to give it up. I also hate to pass up a legitimate deal because I'm suspicious.
Got a picture or a serial number? A good detailed picture would be better. Beware the Chibson's (Chinese fakes) that are out there. They have gotten better and better and unless you know what to look for it's easy to get stung.
get serial no.

contact police asking if a guitar with said serial has been reported stolen

if not, score! but then check to see if fake, as Rickholly74 says - fakes are getting better

if stolen, rat out the shop, claim reward. profit.
Belief is a beautiful armour but makes for the heaviest sword.
Search for the serial number in Google, if you find it in a "is this a fake?" type place it's a fake. Otherwise, if it's not from a private seller, then you're most likely good. From a private seller then you've got to do your own assessment to decide if it's too good of a deal.
Ive seen more and more Chibsons and Epyphonies on the rise recently. just make sure to grab a couple pics on here before you decide to pull the trigger.
I shouldn't post when drunk..

15 Jackson SLATHX-m 3-7 Slime green
Squier std tele (modded to hell)

Engl Powerball
Laney Ironheart 60h
Zilla Superfatboy 2x12 v30's

I would be looking at pics of the serial number, the back of the guitar and the neck binding.

A lot of early fakes had the cavity cover plate wrong - the top not parallel to the centre line of the guitar. Also, I haven't yet seen a fake with Gibson-style crenelated neck binding - but that doesn't mean the fakers haven't rectified that.