Nickelback/Tear Jerker

That's right. Even this rock band has a few emotional songs.

"Gotta Be Somebody".

"'Cause nobody wants to be the last one there
'Cause everyone wants to feel like someone cares
Someone to love with my live in their hands
There's gotta be somebody for me like that...
"'Cause nobody wants to go it on their own
And everyone wants to know they're not alone
There's somebody else that feels the same somewhere
There's gotta be somebody for me out there..."

Also, "Far Away". Anybody who's been separated from their love by distance can relate.
"Savin' Me". The music video makes the already gut-wrenching song even worse.
Also, "Never Gonna Be Alone". Just...watch the video.
The 9/11 remix of "Hero", which uses the "quotes played over the music" technique.
"Lullaby", Especially the Music Video, by they way, the song is really about suicide, not a man coping with his wife's death .