As with many parts of a college application.... it depends!  The goal of admission testing is to help institutions better evaluate the ability of a student to succeed at their particular institution.  Many large public institutions use this data as part of a matrix for automatic admission - based upon prior institutional history.  Selective institutions may use the data to confirm the story which a  student transcript is already telling.  Many institutions are now "test optional" - as they search for more holistic ways to select students.  Just recently, the University of Chicago announced that they will no longer require admission testing, as part of their efforts to diversify their student population.  This move is yet another recognition that students may show their ability in a variety of ways.

Remember.... an admission test score is one facet of the application picture, not a single credential on which to "hang your hat".  If required by the college, do your very best on the test.  You will want it to be an accurate assessment of your abilities.  Follow this goal with all parts of your application... colleges want to see the real you!