Some good ones listed so far.
I’ll add;
Landslide Fleetwood Mac - Haunting music, lyrics, and vocals. Just a great song
Scared The Tragically Hip - Another great song that really just needs to be listened to, not sung along with.
Pachelbel’s Canon - Yeah, yeah, I know. Totally overplayed and overpopular. There is a reason it’s so popular though, it’s simply sublime.
oh, and
I Will Always be Beat Down - John Frusciante
Good stuff 
Ditto on Nightswimming by REM. Also:
Fred Jones pt. 2 by Ben Folds
Tell Her This by Del Amitri
Hallelujah by Rufus Wainwright or Jeff Buckley
Blackbird by the Beatles
Trouble by Coldplay
Come Here Boy by Imogen Heap
OLP’s “Innocent”
From BoardReader, here’s a thread that was lost in The Winter of Our Missed Content:
Classical songs that bring tears to your eyes
One of my recommendations from that thread: the duet from Bizet’s “The Pearl-Fishers”, “Au fond du temple saint…Oui, c’est elle, c’est la deésse”. Used in the film “Gallipoli”.
Nick Drake, River Man
The Beatles (John Lennon), Julia
The Beach Boys, In My Room
Simon & Garfunkel, Scarborough Fair
Stevie Wonder, You and I
Cast of Godspell, By My Side
The Flamingos, I Only Have Eyes for You
Wilhelmina Wiggins Fernandez, Aria from La Wally
When You Dream - The Barenaked Ladies
Both Hands - Ani Difranco
Somebody’s Crying - Chris Isaak
The Shining - Badly Drawn Boy
I’m sure there’s more, but thats all for right now.
Oh - I forgot:
It’s a Motherfucker - the Eels
Sounds like it would be funny, and for about the first 5 seconds it is, then you realize its about the most beautiful and sad thing you have ever heard.
I agree with meyer on the Eels song.
I got quite the list so bare with me
The Anathema List:
-A Fine Day to Exit (song and entire album)
-Barriers
-Deep
-Everwake
-Inner Silence “When the silence bekons, and the day draws to a close, when the light of your life sighs, and love dies in your eyes, only then will I realize, what you mean to me…”
-Parisenne Moonlight
-Release
Ani Difranco - She Says, You Had Time
Coldplay - Trouble, Yellow, In my Place, Don’t Panic
Flowing Tears - The Day You Took my Breath
Billie Holiday - Gloomy Sunday
Louis Armstrong - What a Wondeful World
4 Non Blondes - What’s Up
Alice In Chains - I Stay Away
David Bowie - The Man Who Sold The World
Pearl Jam - Jeremy
Pulp - Common People
REM - At my Most Beautiful, Loosing My Religion
Paradise Lost - One Second, Say Just Words
Stone Sour - Bother (This is the only big-time radio played song I like)
The opening song for American History X ( I have no idea what it’s called)
Blind Melon - No Rain
Dave Matthews Band - Crash Into Me
Martina Sorbara - Bonnie & Clyde II
Meatload - I Would Do Anything for Love
Soul Asylum - Runaway Train
The Turtles - So Happy Together
Stutterfly - Gun In Hand
Moby - Landing
Foo Fighters - Tired of You
Telepopmusik - Breathe (such a relaxing song)
That’s all I can think of at the moment
hehehe
I’ll post more when I think of them…
“Adagio for Strings” by Samuel Barber is absolutely gorgeous, as is “Prayer of St Gregory” by Alan Hovhaness. An orchestra I play in had the good fortune of performing the latter piece at one of our concerts last year. It’s amazing and heart-wrenching and lots of other good adjectives.
Also, I like “Fixing Her Hair” by Ani Difranco and “The Heart’s Cry” from Riverdance.
Steve Goodman - The Dutchman (Which he credited to Mike Smith.)
Great sentiment, a great love, and a great song.
Tris
Landslide by Fleetwood Mac
Ode to my Family by The Cranberries
Mozart’s 23rd Piano Concerto, K. 588… also his Sinfonia Concertante in E-flat major, K. 364
I came up with some more, if that’s okay.
The Who: Behind Blue Eyes
The Beach Boys: Caroline, No
Don Henley: New York Minute
R.E.M.: Drive
The Beatles: Golden Slumbers/Carry That Weight/The End
Bob Segar: Turn The Page
Bon Jovi: Wanted Dead Or Alive
Poison: Every Rose Has It’s Thorn
Poison: Something To Believe In
Saigon Kick: Love Is On The Way
The Black Crowes: She Talks To Angels
Bruce Springsteen: Born To Run (the acoustic version on the Chimes Of Freedom EP)
Bruce Springsteen: Trapped (Live) on the USA For Africa album
Mason Williams: Classical Gas
REO Speedwagon: Keep On Loving You
The Cars: Drive
Benjamin Orr: Stay The Night
Benny Mardones: Into The Night
Richard Marx: Right Here Waiting
Richard Marx: Hold On To The Nights
Marvin Gaye & Tammi Terrell: Ain’t No Mountain High Enough
Diana Ross: Ain’t No Mountain High Enough
Willie Nelson: Always On My Mind
TigoleBitties, I think it’s Nick Cave and the Bad Seeds. Nick Cave is a very dear favorite of mine. From him, “God is in the House”, “Time Jesum Transeuntum, et non Riverentum” and “Are You the One I’ve Been Waiting For”.
The Beatles – “I’ve Just Seen a Face”
Einstürzende Neubauten – “Sabrina”, “Stella Maris” and “Redukt”
Nina Hagen’s renditions of “Ave Maria” and “Der Wind hat mir ein Lied Erzählt”
Portishead – “Kissing the Day” and “This Time Last Year”
Velvet Underground – “Pale Blue Eyes” and “New Age”
The entire album Songs of Faith and Devotion by Depeche Mode
Nearly anything by Björk and Tori Amos
Yellow by Coldplay- Just listen to this song with no distractions. You can feel the love…
Epiphany by Staind- Slighly depressing maybe but also really powerful.
Wonderful World by Louis Armstrong- an old favorite of mine.
Freshman by Verve Pipe- Very powerful.
“Dumb”–Nirvana.
William Orbit does a great version of this. And I just love love love the Ferry Corsten remix.
I’ll toss in another: Glory Box by Portishead.
“Out of My League” by a nearly-unknown group called Stephen Speaks
You MUST MUST MUST listen to this.
“All These Things” by the same group
They have 'em available for download on their website – www.stephenspeaks.com
I second (or third?) the nomination for “All I Know” by Art Garfunkel
“When Somebody Loved Me” by … um … just slipped my mind. Anyway, it’s from Toy Story 2. (Go ahead, laugh. But listen to it!)
My favorite for 46 years: “Moonglow and Theme from Picnic.” The two are combined into one piece on the Picnic soundtrack.
2nd place is the original “Girl from Ipanema.” I’m wild about any Antonio Carlos Jobim bossa novas.
3rd place: Pink Floyd’s “Great Gig in the Sky” for DSOTM. Listen to it while you go for a late night ride with the top down.
Barber’s Air on a G String – although the title makes me titter.
Rhapsody in Blue and An American in Paris by Gershwin.
Are You Going With Me? by Pat Matheny was the only music at my wedding and the title is engraved inside my wedding band.
PLEASE don’t make me stop! I haven’t gotten to opera or jazz yet!
Oops! No wonder it made me titter. It is Adagio for Strings instead of Air on a G String!