There's many ofc. the ones I think of now, that I cry to is a song called "Shoreline" by Broder Daniel, lots of memories in that song.
"Hope there's someone" by Antony and the Johnsons, a friend played it to me once, it was the first time I ever heard anything by AatJ, we both cried like babies.
The song "Mmm mmm mmm mmm" by Crash Test dummies (try say that without sounding like an idiot), there's just something about that song that breaks my heart.