A lot of Radiohead albums are full of this, especially OK Computer:
"Exit Music (For a Film)". It was written for a Romeo and Juliet adaptation, so the Tear Jerker quality is imported from a much older source. The broken-sounding, raw vocals at the end are especially gut-wrenching.
Some people can feel melancholy from listening to "Karma Police".
The little moment of peace at the end ("Such a pretty house, such a pretty garden") just increases the Tearjerkiness.
"Lucky" in itself has a somber, heart-rending effect, but when set to a war child video, the song takes an entirely new light.
RAAAAAAAAAAAAAAIN DOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOWN.... RAAAAAAAAAIIIN DOOOOOOOOWN, COME ON RAAAAAAAAAAAIIIIIIN DOOOOOOOOOOOOOWN...... ON MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE...................
"Let Down". Just..."Let Down". As if the subject matter isn't melancholy enough, this troper considers the "You know where you are..." bit to be one of the most heart-breakingly beautiful moments in music history.
The Tourist. "Hey man, slow down... slow down..."
"Fitter Happier" never fails to bring certain people to tears. The line "Baby smiling in back seat" can be especially triggering.
"Motion Picture Soundtrack", from the end of Kid A, has a similar air of desperation to it.
"How to Disappear Completely" is even worse.
"Fake Plastic Trees", "Street Spirit (Fade Out)", and "Let Down".
The lines "One day I'm going to grow wings / A chemical reaction / Hysterical and useless" from "Let Down" deserve special mention.
Thom Yorke himself has admitted that Street Spirit is one of their darkest songs with no hope at the end, and says that the only way he can play it without breaking down is emotionally detaching himself from the song.
The former is even more of a Tear Jerker in Brazil, where it was the soundtrack for a PSA on Down Syndrome.
There's a lot of great lines in "Fake Plastic Trees" but especially heartrending is the final verse: "she looks like the real thing/she tastes like the real thing/my fake plastic love /[...]and it wears me out/it wears me out."
And not to mention, "And I can't help the feeeeeeling/ I could blow through the ceeeee-eeeeiling/ if I just turn... and run."
"You and Whose Army" stands out especially, although it might be closer to Awesome Music.
"Harry Patch (In Memory Of)" was written as a tribute to Harry Patch, the last surviving soldier to have fought in the trenches during World War I, who has recently passed away.
"All I Need" is definitely incredibly melancholy and apathetic.
And try to watch the video for that song, made by them and an alliance with MTV against child labor (Can't remember the name)
"Talk Show Host" can often leave some people feeling depressed.
"Go Slowly" and "Last Flowers to the Hospital", off of the extra In Rainbows disc, are both incredibly melancholy and beautiful.
Then there is "Four Minute Warning".
"Bulletproof... I Wish I Was" can usually tug on one's heartstrings.
Seriously, don't listen to that song in a depressive mood. Its just... overkill. That song is extremely sad.
"Lewis (Mistreated) has a very catchy and upbeat riff, but the depressing lyrics convey a different message. One of the lyrics is "don't do it, don't, jump." Thom Yorke even sounds like he's crying (or at least very distressed) when he sings this.
It doesn't help that Thom pauses right before he says "Jump", which might imply he did jump.
The band's music tends to get used in heartbreaking Public Service Announcements like this and this
The beginning of "Cuttooth." It's not so much the words but the longing way Thom sings it.
The live version of "Fog." "Where did you go bad...? Did you go bad...?" *sniff*
Oh sweet God, "Pyramid Song." "...and we all went to heaven in a little row boat | there was nothing to fear, nothing to doubt..."
In the "Live in Praha Concert", Thom dedicates it to Franz Kafka before they play it. The live version featuring Jonny's bowing of his electric guitar makes it all the more haunting. ;~;.
The video just about matches the depressing lyrics. Computer animated, we're introduced to a man standing on the roof of a skyscraper in the middle of an ocean, revealing he's the last survivor of a flood that destroyed his city, and possibly the rest of the world. Suitng up, he dives into the water and observes the city's sunken ruins. In the end, he swims into what is apparently his family's house, takes a seat, and unplugs his oxygen cord so he can rejoin his loved ones. Quite possibly the most amount of emotion you'll ever feel for a CGI stick figure.
"A Wolf at the Door". While it's not as slow and melancholy as most of the songs on this list, it is sung with incredible bitterness and desperation. You can't help but feel the pain in Thom Yorke's voice.
"Let me back / Let me back / I promise to be good / Don't look in the mirror at the face you don't recognize / Help me, call the doctor, put me inside"
During certain live performances of the song, Thom Yorke actually lies down and curls up in a fetal position during the post-chorus "no no no no no no no no"s.
"Give Up the Ghost," off of The King of Limbs, is rather tearjerky.
The version from the In the Basement video album outdoes the album version's tearjerkiness by a mile.
"Codex". Pretty self-explanatory as to why.
"Sleight of hand / Jump off the end / Into a clear lake / No one around / Just dragonflies / Flying to the side / No one gets hurt / You've done nothing wrong / Slide your hand / Jump off the end / The water's clear / And innocent / The water's clear / And innocent"
"True Love Waits." Oh god.
"I'm not living/I'm just killing time..."
There There. Thom just sounds pained at times. And was allegedly brought to tears after hearing the final mastered version of the song.
"We are accidents, Waiting waiting to happen."
The backing vocals to "(Nice Dream)":
"If you think that you're strong enough./If you think you belong enough."
"Harrowdown Hill", Thom Yorke's solo song about the suicide of weapons expert Dr. David Kelly.
It was a slippery, slippery, slippery slope/I felt me slipping in and out of consciousness/I felt me slipping in and out of consciousness
"Black Star" from The Bends. There's something nostalgic-sounding about that central riff that tugs at your heartstrings.
"Last Flowers." It originally was written during the OK Computer sessions, during the height of Thom's Jerk Ass reputation and depression.
I cannot keep up
trodding on people's toes
'snot nosed little punk'
and I can't face the evening straight
you can offer me escape.
"Four Minute Warning," which seems to be about the narrator's home being bombed. The desperate, self-deceiving lyrics add to the effect. "This is just a nightmare/soon I'm gonna wake up/someone's gonna bring me round..."
The climax of "Bones."
"Motion Picture Soundtrack" at the end of Kid A. A sad and almost pathetic reconciliation with the rest of the world after the most alien and emotionally tangled album Radiohead has ever put out. Oh, and the angelic harps are killer. "It's not like the movies/They fed us on little... white lies"
"Scatterbrain" has a rather melancholy sound to it.