In FindStat, the database of combinatorial statistics, the major index of a permutation is http://www.findstat.org/StatisticsDatabase/St000004/. By clicking "search for distribution" there, you will find other statistics that (FindStat thinks) are equidistributed with major index. I get 41 results. As mentioned in a comment above, these statistics are called "Mahonian" in honor of MacMahon.