Some people need to keep in mind the difference between "greatest" and "favorite." Rent and Wicked, for instance, are two of my favorites, but I wouldn't call them greatest.
West Side Story (okay, this is is also my favorite...because it's so great!)
Gypsy (one that's not my favorite...still, it's great)
Fiddler on the Roof
My Fair Lady
Sweeney Todd
Maybe I'd switch My Fair Lady and Fiddler on the Roof at another time...but I'm playing clarinet in a community theater production of Fiddler, so I'm a little biased towards that. (even if I wasn't, it would definitely be at least 4th on my list)
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli