I apologize if I'm repeating any, I can't really keep track, just going by what comes to mind.
Blink 182 - Adam's Song
http://www.youtube.com/watch?v=xmLa_W_afH4
Evanescence - Bring Me To Life
http://www.youtube.com/watch?v=_TILCIRspO0
Goo Goo Dolls - Iris
http://www.youtube.com/watch?v=LQR3P_Righk
Green Day - Boulevard Of Broken Dreams
http://www.youtube.com/watch?v=RJrXt5WVVZk
Jimmy Eat World - Hear You Me (about grief and loss)
http://www.youtube.com/watch?v=scLcUfhd2kY
Jimmy Eat World - The Middle
http://www.youtube.com/watch?v=FV-HPOHu8mY
Nickelback - Never Gonna Be Alone
http://www.youtube.com/watch?v=9oHQhjNkJtI
REM - Everybody Hurts
http://www.youtube.com/watch?v=lh57ACP6bA4
Simple Plan - I'm Just A Kid
http://www.youtube.com/watch?v=jXiV9EhDN4o
Simple Plan - Me Against The World
http://www.youtube.com/watch?v=y3VdqxS8mEs
Simple Plan - Perfect
http://www.youtube.com/watch?v=-9qt_59zoKM
Three Days Grace - Never Too Late
http://www.youtube.com/watch?v=YWapziQ2mAk
I'll try and add more as I think of them.