A whole bunch of stuff but off the top of my head some things that come to
mind are:

Make sure the engine is cold and look for white or blue smoke at startup.

Look at the oil and see if it looks OK.

Look at the transmission fluid (auto trans) and see if it looks nice and red
or brownish.

Check the coolant level--if it's low it could mean a leaking gasket
somewhere.

Check underneath for leaks.

Make sure the CEL is not on and the engine runs smoothly.

Check the overall appearance of the engine, belts, hoses, battery terminals
etc--if they don't look good then the vehicle was probably not well
maintained.

Check the operation of all accessories and lights etc.  If you find too many
things that don't work then, once again, it was not maintained.

Check for uneven tire wear and how much tread is left.  Do the tires all
match and is the spare OK?  Brand new tires could be an attempt to cover up
a bad alignment or shocks.

Ask for service records.

Do or get a compression check if possible.

Drive it.  If it doesn't feel right don't buy it.

The list goes on and on....

In addition to Ulysses' list, I would look all over, in the trunk, etc for
signs of rust or
immersion in water, whether rust has started or not.

I would look underneath for appearance of mechanical damage, condition of
ball joints,
exhaust, etc.

If all okay, I would go to Carfax and see what they had to say.