There are hundreds of such programs and the best place to find them is on the website of the National Center for Fair & Open Testing, generally known as Fairtest. Fairtest's mission goes far beyond helping students and their parents find colleges that don't require standardized tests for admission. They also work on the elementary and secondary level, seeking to "end the misuses and flaws of standardized testing and to ensure that evaluation of students, teachers and schools is fair, open, valid and educationally beneficial."
The Fairtest list presently includes over 800 schools, none of which require SATs or ACTs for all entering students. However, these schools will require such entrance exams for some students, such as international students, or some students who don't meet their grade criteria. In addition, these schools may use standardized tests for placement purposes, for example, permitting students with a score above a particular point to "place out" of a beginner level course.
For students for whom college admissions tests are a barrier to continuing their education after high school, the schools on the Fairtest list -- and they include many excellent programs -- may be more flexible options for consideration.