Many states use the SAT and/or ACT integrated suites of assessments in some capacity for educational testing. Specific state testing requirements notwithstanding, no student has to take the SAT or ACT.
That said, any U.S. student who wishes to apply for admission to one of the colleges or universities that requires test scores as part of the application–meaning most of them–must take one or both of these exams and submit test scores.
Furthermore, a student does not have to take the SAT or ACT on any specific test date, again notwithstanding state testing policies. Both exams are administered multiple times throughout the calendar year, affording test takers plentiful options. In contrast, the PSAT is only offered on two dates in mid-October.