As with almost everything else in college admissions, it depends! Are you applying Early Decision to your dream school where your GPA and test score exceed the 25-75 percentile range? You might only need to pick two or three backup schools. Are you shooting for the moon and applying to schools with very selective (<30%) selection processes? You might want to cast a wide net, with at least five such schools, plus three where the acceptance rate is between 30-50%, plus a true safety school.
Sometimes, students go too far. There is very little reason to apply to more than fifteen schools. Biting off more than you can chew might drag down the overall quality of your applications, counterintuitively limiting your options when the acceptances roll in.