The obvious things are:

• Where did they get it
• Why are they selling
• Have they had any problems
• What work has been done to it whilst they've owned it

Basically, though, I think you can ask them almost anything about the car and just see if the lie to you or not

If it's a private buy then I tend to judge the person who's selling it almost as much as the car; nice, well-kept home is good, but multiple cars parked up, spray cans discarded in the garden then it's a no. I'm not bothered about why they say they're selling it, but I am interested in any history and the longer it's been owned, the better. One quick check is the tyres - if they are all the same manufacturer and type, that's a very good sign. And i also am prepared to walk away if anything is amiss - there are plenty other buys out there, even in a heated market. Good luck.