From the 2011 statistics, the average person who matched ranked 11 programs, but once you rank 8 you're already at about 95% change of matching. Almost 100% when you rank 15.
Personally, my goal was to interview at 10 programs and rank at least 8. I ended up going on 13, which I think was overkill. Particularly for me because I had a home program that I liked and I think ended up ranking around #5-7, which meant all the programs I ranked after that pretty much didn't matter (since my program liked me). I also matched well, so hindsight is 20/20 I suppose. Could've saved a lot of travel money...
But you never know for sure how you're going to match. And I think if you have an interest in a program, and you have the time/money, it's worth checking out more programs just to see what else is out there--you never know when a program will really surprise you.
Either way, if you're nervous about matching (like I was), I'd aim for a higher number of programs. I personally think 15 interviews is a very high number, but maybe it's just me. I do know some people that interviewed at more than 15. If you're a really competitive applicant and confident, then you should be able to get away with less.