The Key Is To Create Options For Yourself
I know of a few students who will only apply to three schools this year. They have done their research by visiting the campuses, they understand their admission chances, and they have spent a lot of time seriously considering their college choices. These students know their chance for admission is very high (based on their test scores and GPAs) and they know that each campus will fit who they are as individuals quite well. Regardless of which school (or schools) admits them, they have options in which they feel confident and excited about.
On the other hand, I also know of many students who will apply to eight or ten schools this year, simply because they want MORE options. And there is nothing wrong with this. I encourage students to cap their applications at about 10, as many more than ten can get very overwhelming. If you've decided to apply to several schools, it's important to be sure that you have back-up options. Apply to schools that fit who you are as a student and as an individual. Is your dream school slightly out of your reach? Apply anyways, but also apply to several "safer" options, as well.
The point is: there isn't a magic number of schools that any one person should apply to. Do your research and understand the type of schools you're considering. Study the averages and trends for previous incoming classes to help you better understand your chances for admission. And remember: Always, always be sure you're creating options for yourself!