I want the Good Times Back- from The Little Mermaid
I know it was in the Broadway production, but it has been cut and replaced in the Netherlands production, which is supposed to be the revised "perfect" production.
Build a Wall- Shrek
Once again was in the Broadway production and was cut from the West End version. It was my favorite song in the show and one of the few character driven songs in the entire score. Its a great men's power ballad, which we don't hear very often even if it sounds like "Free Fallin'" by Tom Petty
I've always really loved All Things Bright and Beautiful and Who Could Be Blue/Little White House, both cut from Follies.
I've heard/read that there are alternate lyrics to Little White House than the ones that can be heard on most recordings. I believe they've been described as more cynical - i'd love to read them sometime. :)
"The gods who nurse this universe think little of mortals' cares. They sit in crowds on exclusive clouds and laugh at our love affairs. I might have had a real romance if they'd given me a chance. I loved him, but he didn't love me. I wanted him, but he didn't want me. Then the gods had a spree and indulged in another whim. Now he loves me, but I don't love him." - Cole Porter
"I Want the Good Times Back" from The Little Mermaid. Such a shame it was replaced. "Love and War" was hilarious too, especially when some random Harvard dude walked by and saw Elle talking to herself.
I love "Pleasant Little Kingdom", which originally lead directly into "Too many Mornings" in FOLLIES. You can hear John McMartin and Dorothy Collins do in on the first Sondheim Tribute album (the "scrabble" album).