It takes not just a piece of music, but a real performance to do the trick. I heard Ivan Fischer conduct the Budapest Festival Orchestra in the BBC Proms in 2004. They played Rachmaninov 2nd Symphony, and I had no idea that orchestras could still play like that. I wept throughout. No other performance of the work has ever done that, though Rachmaninov has a magical way of making one feel like a friend.
Phyllis Sellick, one half of the Cyril Smith and Phyllis Sellick piano duo for many years (they were married) was interviewed on the BBC a couple of years ago. She remembered being at the Proms in the 1930s, when Sir Henry Wood premiered Vaughan Williams' "Serenade to Music", which had been written for his 50th anniversary as conductor. In the first half of the concert, Rachmaninov had played his own 2nd Piano Concerto, and in the second half, he sat in a box, just in front of Phyllis Sellick. Apparently he chose to leave the hall soon after the Vaughan Williams started, because he was crying. I was rather happy to hear this story, because it confirms all that I love about Rachmaninov.
Oh, and by the way, since I met and got married to the woman of my dreams, I find it easier to cry. Aahhh!