*mileage on used car: find out if highway our in-city driving....obviously, highway miles are much less 'demanding' on a car
*type of car: most 'popular' cars have cheaper parts, find out what parts would cost if they break, for example, my buick lesabre is fairly cheap in the midwest
*tire wear, would you need new tires soon
*has oil been changed often and regularly (not sure how you can check this though)
*heh.......'back seat' room (if you *need* it, as i never seem to...)
*gas mileage is sorta important, but if you want a truck or suv, just ignore it, it's just gonna be crappy
*warranty left on car? is it transferrable to new owner? ( i think most are )
*leasing or buying....if for long run (you want car for years and years) make sure you have a v6, not a crappy v4, as a v4 has to work sooo much harder to get a car moving, the v6 will last longer in the long run (some newer and nicer cars this won't apply to, like hondas, their v4's are pretty darn good)....but if you're leasing, a v4 would be fine, as you won't keep it forever
*from last point, was car a lease or buy? if a lease, the previous 'owner' might have run it hard, not caring as they would not keep it....(don't know how to really check for this either)
*brake wear....the dealership should take care of this....if you buy from dealer....if straight from owner, ask if they ever replaced the breaks
*when you drive and go up hill, see if car likes to downshift often, it's a sign that the car does not have much power...it gets annoying on small cars w/ small engines....and bad for tranny
hope this helps, as i'm not that good at cars myself, but it's things i look at...
-sandlizard