Isla:
Thanks for the offer. I might take you up on it! I see you are in No City, Florida! The world's favorite tourist destination!! Anyway, yes, Henry Mancini. Met him at the Kennedy Center with a bunch of other well-known people (what was I doing there?). He was very ascerbic. Not as friendly as he looks from a distance.
Regarding John Williams, he is popular because of his movie scores principally, but I don't think he can hold a candle to guys not in the original survey (what survey?) like Sibelius, Holst, Rachmaninoff, and Shostakovich. We haven't even mentioned Orff, and only Isla has mentioned Ravel and Bartok. Skriabin is certainly NOT very popular among the generally public, but was a talented composer. One friend calls him Screechabin. PianoMan, being a piano player and liking dissonance, WOULD love Skriabin. Some of his work is very difficult to play and listen to. And then there's Nicholas Cage, who is very inventive. I just can't see John Williams being a top tenner yet, but if we get this survey fixed today, I'll stick him on the list. I agree with Sohcan on that score, so to speak.
Pink Floyd would be very difficult to justify to the Chairman of a Music Department at a major university, but I love their music. They are off-genre anyway.
And what about Strauss? 2001, and nobody is pining for Strauss?

Der Rosenkavalier has no fans here? I would put him way above Williams, but maybe I need to listen to less Strauss and more Williams.
PianoMan: As a whole, I agree about the 20th Century. My favorite composer is still Mozart and my favorite piece is actually Dvorak's B Minor Cello Concerto. Zoom, da da zoom!
yakko: Debussy made my top 10.
Dennil: I'd take Saint-Saens and Aram Khatchaturian ahead of Williams, I think.
Interesting thread for a failed poll!