Fiddler is indeed a classic with some of the best loved Broadway hits of all time. The story too is compelling and provoking as are the religious themes if one is predisposed that way. I will have to confess, however, that unless very carefully staged and directed, there are places in Fiddler that can become slow and bogged down--the story doesn't flow smoothly pulling you to the next scene--and that might prevent it from ranking the all time best. The modern remake of Phantom of the Opera suffered the same kind of flaw.
For modern musical/opera, however, Evita was very well done.
True story: My sister in law and her lady friend won a trip to a convention in NYC--both small town girls and their first trip to the East or really much out of Texas and surrounding states. So here they were in a big hotel in Manhattan on their one free night and thought it would be fun to see a broadway show. The desk clerk was helpful knowing they would only get tickets to an obscure off broadway production at that late date, but Sis-in-law requested tickets to Fiddler. It was six hours before curtains up and the desk clerk snickered but humored them and began to dial as sister-in-law prayed fervently, "Oh Lord, let us see Fiddler." The desk clerk hung up the phone with a strange look on his face. The theater had just had two cancellations and sis-in-law and her friend got them. You could almost hate somebody with that kind of blind, stupid luck.