The overture to Rags -- which wasn't used in the production, I was recently reminded (and I saw a preview) -- never fails to wring a tear. I often listen to the whole show on July 4th. It's perfect.
And "If We Never Meet Again," which has several iterations in Rags' many revisions, is lovely on the first post-Sideshow Ripley-Skinner album of duets. Probably my favorite version.