Two dozen public universities cracked the top 100 overall in this year’s Wall Street Journal/Times Higher Education College Rankings, even as the privatization of public education passed a significant milestone: Students in a majority of states are now paying more in tuition to attend public colleges or universities than the government contributes.

The top five public schools varied little from last year. The University of California, Los Angeles again led the pack, at No. 25 overall, followed by the University of Michigan...