It should be doctor's.

I can see how the possessive could be confusing if you are only thinking about it from your side, but don't forget that the doctor also has an appointment at that time - with you.

Hmmm.  The responses here surprised me because "I have a doctor appointment" does not sound "wrong" to me -- I would be just as likely to say "doctor apppointment" as "doctor's appointment". Does anyone else agree with me?  Maybe it's a U.S./U.K. difference?  Or am I just weird?

How about "I have a dentist appointment"?  I might either say it that way, or say "I have a dental appointment."  Is anyone going to make a case for "I have a dentist's appointment"?

Hi,Hookster -welcome to the Forum.  There was actually a long discussion a while ago about "a pair of pants" -- apparently pants actually used to be two separate pieces, kind of like cowboys' chaps, that tied together at the top.  I understand why English is hard to master, but I thought I had done a pretty good job of it in 52 years, which is why I was surprised to find that something that seemed perfectly natural to me was consedered "wrong."  Perhaps I should have added that I would probably not write "doctor appointment" in anything formal -- I agree that "doctor's appointment" sounds more formal - but in conversation "doctor appointment" sounds perfectly fine to me.  (This would also explain why it shows up less often in  The New York Times.)

Grammar Geek, would you like to venture an opinion on this one?

Hookster, what part of Colorado are you in?  And, to digress a little, do you consider yourself a Coloradan?  I am pretty sure that when I was growing up in Denver we were all Coloradoans -- then I spent 20 years on the East Coast and returned to find that I had lost an entire syllable.