I applied to seven schools, most of which had professors that I was specifically interested in working with. It felt about right at the time but now it feels like way too many, especially since I think I've made up my mind about where I really want to go. I guess it's hard to gauge where you stack up against the other applicants and so that might lead to applying to more schools than necessary. It's hard to know whether there will be a lot of other qualified applicants who want to work with the same professors!