I think it varies a lot. I'm going to 8. I have friends going to 9, 7, 2, 1 etc.
I'd love to hear statistics from everyone else as well!
I'm going to 6, got 8 offers, applied to 14 (still have 1 to hear from but assuming a no at this point / would have to turn down anyway). Most programs I'm looking at are only 1-3 spots, hence applying to sooooo many.