A lot depends on what you are going to use the horse for and how old the horse is.
Certainly you want to ask about the medical and training history, current/previous use of the horse, and any diet concerns.
If it's registered, make sure you actually see the certificate.
If you don't know the owner well, ask for references, too.
You may want a pre-purchase vet check if you have any medical doubts. Having an experienced instructor/trainer look also can help insure you get a good match to your skill and planned use.
Alot can depend on each horse, but here are the questions I always asked
1) has the horse ever been lame?
2) has he ever coliced?
3) any health problems?
4) any bad habits or vices?
5) any known health problems that his parents had?
6) does he clip?
7) how is he with bathing?
8) does he stand for the farrier?
9) does he stand for the vet
10) how is he in a stall?
11) does he require any special supplements or feed?
12) what skill of rider does he require?
13) any professional training?
14) ever been to a show?
15) if yes to the above, any ribbons?
16) how often is the trimmed?
17) when was the last time his teeth got floated?
18) when was the last time he had his sheath cleaned (take this one away if you are looking at a mare lol)
19) Is he up-to-date on all shots?
20) when was the last time he was wormed and what worming medicine was last used on him?