There is no general number. I know people who apply to 1, 3, 5, or even 10+ schools. Some do 3 in R1 and 3 in R2. Some just try to secure something at an early decision type of program like Columbia or Duke. Some just throw that big net and hope to catch many.
You need to figure out why you are applying to the schools (the positive vibe you get from the alumni? know people there? location? curriculum? teaching style? type of jobs/recruiting companies offered? reputation? ranking? your chance of getting in? your chance of securing a fellowship or loan there?........). The bottom line is the school (whichever you end up going) should help your career... your application strategy should have some "reaches" some "reasonable shots" and if you must go to school this year, perhaps 2 "safeties."
My reason of applying to the schools will be different from yours. My "reaches" and "reasonable shots" will be different from yours. The number of schools I am applying to will be different from yours. | 
