Nutshell and Would? by Alice in Chains
Indifference by Pearl Jam - just the melody of that song sucks you in
Blue Christmas - Elvis. Was played at my uncle's funeral, was really close to him, he died way too young, and in December. Elvis was his favorite and that was his favorite Christmas song. So its emotion of a personal level, not an artistic one, but still
The Rain Song - Led Zeppelin. Don't know the message but the melody is just enthralling. Plus its probably one of the few real original creations by the band, so that's a positive as well
Landslide - again, cheesy, but both the Stevie Nicks version and the Smashing Pumpkins versions are good
Smashing Pumpkins have a few good ones too. Not the biggest fan of the band, but 1979 and Tonight are both moving. Was amazed to learn that "Today" is about a suicide attempt; it changed my whole perception of the song.
Nuvole Bianche - Ludovico Einaudi
Also a song called "Tomorrow" by Salif Keita. It was used in "Ali" for the final fight. Really powerful scene. Amazing song. Lots of songs I guess are emotional to me because of their attachment to particular movies. Like "Raglan Road" from In Bruges. That scene is quite sad, plus when I actually got around to listening to the lyrics, it became personal, as I'm sure it would be for anyone.