For my first mare, I made 3 visits. For my gelding I made the mistake of only visiting once (although to be fair, I'm not sure the issues I had with him would have been discovered even after several visits).
Right now I'm horse hunting and am making my third visit this weekend. I'm thinking that one, then going out for the vet check, for a total of 4 visits, should be enough to have a really good feel for whether he's the right match.
(The problem is that I already think of him as "mine" I'll be pretty devastated if it doesn't work out at this point )
What do you think? How many times does it take before you feel comfortable that you've seen enough of the horse in enough different situations to make him/her your own? How many times did you go see your current horse(s) before making an offer?