[Comatose]

Look over the engine bay closely and look for anything out of the ordinary. Crawl under the car, look for leaks, anything unusual--dents, severe scratches, wrinkles from a potential accident, etc. If it's a hatch, pull up the rear carpet on both sides and take a look around.

I spent over an hour looking over my car when I bought it, the lady at the dealership gave me some weird looks when I crawled under the car six or seven times. Take the extra time before you make the trade, that was your less apt to come across any surprises.

Finally, see if the previous owner has any service records or reciepts.