Some great points brought up here.
Jon has a great point about West Side being in Tick Tick Boom...a bit of it is also included in Avenue Q(and it's acknowledged that they took that bit from WSS), in Purpose: "Could it be, yes it could, something's coming, something good"...from "Something's Coming." Still influencing musicals a lot today.
In terms of influential musicals, obviously Showboat and Oklahoma are right up there with WSS, and again arguing the little nitpicky points about which of those is most influential is ridiculous (though I was thrilled WSS was voted most influential

) Influential certainly plays a part but is not the only thing that acknowledges best I think. Take Oklahoma. For the time it was made, it was groundbreaking and EXTREMELY influential. No matter my feelings on the show, I can't deny that. But I wouldn't argue it as one of the best musicals--the dream ballet is much better executed in WSS for example. Then again for the time, it was pretty amazing, and one wouldn't fault that for example. It's hard but I think if we're just talking "best" we need to let time play a bit of, but not a huge, factor. Showboat I mean was obviously fantastic for its time, considering there were no musicals w/ plots around, but obviously it has its flaws.
ABoyLikeThat, the only show I've ever heard perhaps described as "perfect" is Gypsy, and...this is totally another thread, why I think personal bias comes in when picking the one best, but I personally think WSS's amazing score and choreography makes up for its small flaws to be on Gypsy's level. Gypsy aside, what shows would you call perfect and please explain their perfection.
I'm not sure where dancing comes into play. A great musical doesn't have to have dancing, but it can be important. Maybe when you get up to the best of the best, some shows are so close that one having amazing dancing and not having any separates them? I don't know. I feel like it doesn't influence the greatness of any show, but when you're comparing, the show that doesn't have dancing has to surpass the other show in other elements maybe?
And let's be honest. My 3 favorite shows are West Side Story, Wicked, and Rent. I pretty much equally love them all for different reasons. I "get" Rent and Wicked, I acknowledge their positive aspects. But if I'm arguing the best show, I cannot overlook their flaws. I still love them, a LOT more than Gypsy as I've already mentioned, but there is no question in my mind that Gypsy is a better musical.
Finally, I'd like to hear more arguments than just answers. Those of you who have said you wouldn't even consider West Side Story as one of the best, please explain why. And I know arguments for Gypsy, but would like to hear more in-depths reasoning for some of the others shows you guys have chosen as the best.
BTW, as demonstrated by my signature...I am absolutely loving reading some of the comments said here
"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