R.E.M./Tear Jerker

Pretty much the whole of Automatic for the People.
- There's "Everybody Hurts". Specially the video.
- And "Nightswimming".
- And "Find the River".
- And "Sweetness Follows".
- And "Monty Got a Raw Deal".
- And "Try Not To Breathe".
- As well as "The Wrong Child". Interestingly, Michael Stipe has never actually admitted to what the song was about -- but it paints a vague picture of a child who is handicapped and separated from his peers.
"I'm Not Over You", a small song stuck at the end of "Diminished" on Up seems so tortured. Stipe plays the guitar and sings a few lines about a failed relationship. Something in his voice and that half-hearted guitar-playing...
"Let Me In", which is dedicated to Kurt Cobain, is very sad. It can be even worse seeing it live, because the guitar for the song is the actual one Cobain used to own. Heartbreaking.
"Drive" is more haunting than straight-up sad.
"Man on the Moon" can result in Tears of Joy.
"Wendell Gee".
"E-Bow The Letter", which is dedicated to River Phoenix, most certainly counts. Especially the live version featuring Thom Yorke.
Out Of Time gives us "Half A World Away" and "Country Feedback"