I'm only applying to two schools, though I wouldn't recommend it.
Those two would be a school on the low end of the top 40 (my dream school though as I specifically want to work with a professor there) and my current institution. I'm only applying to two because all I've got going are an incredible improvement over the past year, solid letters of rec from fairly unknown professors (who will vouch for my studying Rudin, Mac Lane, Markushevich, Munkres, etc. in my spare time), and experience and a good rep for doing TA like duties (working as a tutor in the Math Learning Center, which is what our TAs do).
Hopefully GRE scores will be a positive addition. I almost feel like making an 800+ is my only shot at getting in my dream school. My current institution is a lock with a TA position though. They just don't have anyone in my field here (complex analysis) and its an applied math school (whereas I love pure math). Ah well.