Most prospective graduate students are advised to apply to at least 8-10 programs. As when applying to undergraduate schools, this should include a mix of “safe” schools, good matches, and “stretch” schools.
Note that these choices depend on the academic reputation of the graduate programs you are applying to, and not the institution as a whole.
Students should talk to faculty and advisers to get additional feedback and suggestions of schools that are good matches with their interests and abilities.
Most programs have an application fee. If these fees would represent a financial burden for you, check if the schools offer waiver programs for students in financial need. Many do.