I'm a bit of an overture whore... so I have several favorites:
As others have said: Gypsy, Amour, My Fair Lady
And I also like: Mack & Mabel, Millie, Light in the Piazza, and even though I basically HATE the stage version, I love the overture to Meet Me In St. Louis. I'm such a dork, I've even staged it...
Wow no other fans of the overture to Promises Promises? I can see how it (the first fully mixed and amplified Broadway show--a mixed blessing I admit) really revved up audiences from the first big notes. I dunno if Bacharach or tunick did the overture but I suspect Bacharach did as he was used to doing instrumental pieces from his movies.
I think it's silly and not playing by the rules for people to pick pieces like the WSS Prologue over traditional overtures but I agree with Styne's Funny Girl and Gypsy being superb as well as Candide and Sweet Charity.
I know more often than not the arranger or the orchestrator does the arranging of the overture--Rodgers never did his own I don't think--Russel Bennett did the famous ones anyway and I believe Tunick even did the superb Merrily we Roll Along for Sondheim
Agreed on the JCS, but it's only second best to me.
The best overture I have ever heard was the intro to the Meat Loaf album "Bat Out of Hell." I know, it's not a musical, but it's a very theatrical album, soon to become a musical in 2007, and I just love the piano intro, and the motorcycle guitar.
"There is no problem so big that it cannot be run away from."
~ Charles M. Schulz
Regarding the Promises, Promises Overture, I believe it's Tunick's work. I've read somewhere that Bachrach was critical of the orchestrations having too much of a Broadway sound, although I think Tunick did an excellent job imitating Bachrach's style. (In the Follies score, there's a tempo marking, I believe for a section of "The Right Girl" that says "a la Bachrach," although that was probably the work of dance arranger John Berkman).
Some composers proposed layouts for their show's Overture, but it's almost always the work of the orchestrator. (I believe though, that the aforementioned Sondheim did actually write his own dance music for "The Cookie Chase" in Anyone Can Whistle, which is somewhat unusual).
Begin at the beginning and go on till you come to the end: then stop.