There is no rule that dictates how many colleges you may apply to.
But students who thoughtfully curate a balanced list of schools tend to have less stressful application processes than those who apply to dozens. They end up with a list of colleges they're exited about, plenty of which are well within their admissions and financial reach. And they feel more in control of their college destiny because they're not at the mercy of admissions decisions from a long list of highly selective colleges.
As you are crafting a list of schools that fit your specifications, include colleges that fall into each of the following three categories: match, reach, and safety.
A match school is one where your academic credentials (GPA, SAT or ACT scores, and class rank) fall well within (or even exceed) the school's range for the average freshman. There are no guarantees, but it's not unreasonable to be accepted to several of your match schools.
A reach school is one where your academic credentials fall below the school's range for the average freshman. Reach schools are long-shots, but they should still be possible (and not a dream). Don't let the sticker price of a financial reach school scare you off! Financial need, academic strength, and a college's desire to have you on campus can all influence your financial aid award and make the cost of attendance more manageable.
A safety school is one where your academic credentials fall above the school's range for the average freshman. You should be reasonably certain that you will be admitted to your safety schools. Like the rest of your list, these should also be colleges you'd be happy to attend. In addition to an admissions safety school, it's a good idea to include a financial safety school on your list, one that you and your family can afford even if you received no aid at all.
Send applications to a few schools from each category (for example, three reach schools, three match schools and two safety schools). Applying to a range of schools will ensure that you set ambitious goals and give yourself some back-up options that don't feel like consolation prizes.