Now? None. I believe they've all done away with it. In the past, quite a number of states. Mine was originally; but, I was able to change it in 1995, when Virginia began offering people the choice of SSN or a DMV number. (It was the result of efforts by the ACLU and others.)

Many states have done all or part of the social security number on drivers licenses. Thankfully not ones I've lived in, but a Google search will yield lists.