There are several better contenders for the '30's honor than "Anything Goes", which is basically a revue. "Pal Joey" was a major groundbreaking show of the thirties (it brought cynicism, sex, and acrid wit to the musical), and "The Boys from Syracuse" is certainly up there as well.
I agree with "Carousel" for the forties, but "Guys and Dolls" is fierce competition.
There's a LOT of competition in the 1950s. I'm going with "Gypsy" (1959) which is tougher, funnier, and more enduring than "My Fair Lady" (which now seems dated and overdone).
And for the sheer brilliance and entertaining sweep of its score, I'm going with "City of Angels" for the 1980s. I don't care if it was overshadowed by the ultra-pretentious "Les Miz" and "Phantom".
"Ragtime" for the 1990s, all the way.
I ask in all honesty/What would life be?/Without a song and a dance, what are we?/So I say "Thank you for the music/For giving it to me."