Here are a few that get to me:
Hiding My Heart by Brandi Carlile. This is the song we had sung at our wedding. It's a little depressing but we love it because it reminds us of our long-distance relationship. Also, we went to a Brandi concert the night before we got engaged, so it's a little sentimental. You can hear it here.
Claire du Lune by Debussy: A classic. Beautiful. Listen to it here.
Somebody Loved by The Weepies. Listen to it here.
There are more, because I always find myself quite affected by music, but those are some of my top songs.