Some schools that don't require the tests for admissions will usually require them for certain majors. My son took the SAT, I've heard that there are some changes coming to the ACT so you may want to find out what those are.
The first time my son took the SAT he didn't study, based on his results and the schools he was targeting we got a good idea of what and how much test prep to do. Some schools will list right on their website what score is needed for certain merit scholarships, so you can easily figure out the ROI of the type of test prep. In most cases a few hundred to a few thousand dollars of test prep can save you tens of thousands of dollars later on.