Some colleges do admit students without a high school diploma or GED. Home-schooled, high school and non-traditional students without a diploma all have opportunities enter college programs.
Home-schooled students who did not receive an official certificate may be able to provide a portfolio of high school work along with their entrance exam scores to gain admission to colleges.
Some technical colleges and schools that cater to non-traditional students have different entrance requirements than schools that focus on recent high school graduates. The federal government requires students without a certificate to pass a test that shows they have an ability to benefit from college-level work, but these schools are open to students who want to learn.