This is only counting Broadway productions, not tours, regionals, London, etc.:
The Phantom of the Opera 71
Chicago 29
Les Miserables 16 (original and two revivals)
Rent 13
Avenue Q 12
Spring Awakening (2006 version) 9
Hamilton 5 (+6 in Chicago)
Not surprisingly, Phantom is the show I've seen the most outside of Broadway too, including London, high school, college, Las Vegas, original tour, and new tour.