Take if for a test ride
Check the chain for any "stretching" (
http://www.sheldonbrown.com/chains.html#wear)
Rear cassette (if the teeth look like shark fins instead of mountain peaks, you'll probably need to change it as it likely won't shift properly)
Is the freewheel working properly?
State of the teeth on the crankset (ala the link above)
Does the bottom bracket make noise?
Does the crankset "wobble" at all?
Is the steering notchy?
Does it change gear easily
Check the brake pads, this can give you an idea on the condition of the bike and how "correct" the owner is.
If it has discs, spin the wheel and listen for any scraping sound as the disc passes through the caliper (checking for warper rotors). Light warping can usually be easily fixed.
Check the condition of the brake and shifter cables..
See how "in-true" the rims (not the tyres) are by spinning the wheel and watching from above and slightly to the side (easy also to determine when you ride it, even easier when you hit the brakes)
Check for broken spokes, wear on the braking surface of the wheels, if the wheels spin easily and freely (or if they bind or slow down too quickly).
How easily does it shift?* (stuck shifters can "usually" be unstuck by spraying a ton of chain lubricant into the STI / mechanism, literally until it's dripping out, wait a few minutes and come back to wipe off the excess lubricant and try the shifting mechanism again several times, working it back and forth.
Check for cracks in the frame (and any potential coverup)
Is the seat post easy to remove / adjust?
Does it make any weird noises when riding?
