I've never been "moved to tears" by music. I don't even think any music has made me actually feel sad or depressed (just angry, but that's a different thing

).
But several pieces have managed to make me sit through a concert with my jar dropped and wishing the music would never end (which also often had to do with awesome performances, not just the composition). The most recent one (last Saturday) was Wolfgang Rihm's "Male über Male 2", others include Xenakis' "Mycenae Alpha", Wagner's "Meistersinger", Bach's B-minor mass, Boulez' "Pli selon Pli", Rameau's "Les Paladins" (William Christie conducted. It was the most opulent opera experience I ever had.), a string quartet by Lachenmann which I don't even remember the name of, and others.