Putting The Damage On, by Tori Amos
Joan Baez singing Swing Low Sweet Chariot in the dark at Woodstock(?)
Baby Can I Hold You, by Tracy Chapman
Fistful Of Love, by Antony & The Johnsons
I can’t even listen to the beginning of Unravel, by Björk without my eyes watering up.
Country music can really jerk the tears, and none better than Kathy Mattea’s “Where’ve You Been?” Except maybe Tim McGraw’s “Don’t Take The Girl.” Or Colin Raye’s “Love, Me.” Or…
Yeah, I have to go now.
I was going to say Foi Na Cruz by Nick Cave - absolutely devastating, I find it.
Exactly what I was going to say, along with his Please Stay.
Ow. I know what you mean. It’s such a beautiful song, and one that really tugs, on so many levels. Mostly because that song is completely wrapped around so many of my long-ago memories, I absolutely cannot listen to it without breaking down in tears. 
Now that I look back on it, I think that hearing it as a young child, I never did understand the last part of the song. It just didn’t affect me then because it didn’t feel real. Now that I’m older and wiser (well, older at least) it just hits me like a ton of bricks. Sigh
“I hope that I don’t Fall in Love with You”
both Tom Waite’s and the gorgeous cover by Natalie Merchant
Yeah, I look at my three-year-old living in his world of perpetual novelty, and I think “A dragon lives for ever, but not so little boys…” sniffle.
Anything emotional by Stan Rogers gets me. “Straight and True”, “Down the Road”, “Lies”, “Last Watch”,… For their sentiment and for everything he didn’t get to create.
I think you mean the song Angel by Sarah McLachlan. It’s a beautiful song, and one of the ones on my list, though Hold On from her third album hits me a bit harder.
Soldier’s Things by Tom Waits is one of the saddest songs I can think of. Someone selling off a dead soldier’s belongings:
*oh and this one is for bravery
and this one is for me
and everything’s a dollar
in this box *
I also agree with the Band Played Waltzing Matilda.
Killkelly
I’ve heard many versions but my favorite is from the Green Fields of America album. The first time I heard it was at an Irish fest. When the singer finished there wasn’t a dry eye in the audience. A couple weeks ago my 14 year old son heard it for the first time. The song ended, he was bawling his eyes out. He told me that if he played it for some of the emo kids at his school that there would be a rash of suicides.
There’s a version by Marc Cohn during The Prince & Me. Hmm, I liked that one but I bet the two you mention are even better.
Harry Chapin’s Cats in the Cradle
… And the cat’s in the cradle and the silver spoon,
Little boy blue and the man in the moon.
“When you coming home, son?” "I don’t know when,
But we’ll get together then, dad.
You know we’ll have a good time then.
Marianne Faithfull’s Ballad of Lucy Jordan
At the age of thirty-seven, she realized she’d never
Ride through Paris in a sports car with the warm wind in her hair.
So she let the phone keep ringing, and she sat there softly singing
Little nursery rhymes she’d memorized in her daddy’s easy chair … .
Sarah McLachlan’s When She Loved Me
So the years went by
I stayed the same
But she began to drift away
I was left alone
Still I waited for the day
When she’d say I will always love you … .
Eric Clapton’s Tears in Heaven
Would you know my name
If I saw you in heaven
Will it be the same
If I saw you in heaven
I must be strong, and carry on
Cause I know I don’t belong
Here in heaven … .
Absolutely. I can’t bear to listen to it as an adult.
…Patty Loveless’ How Can I Help You To Say Goodbye, or Sherrie Austin’s *The Streets of Heaven.
*
Yep, time to get the Kleenex! sniffle
Not sure why but Michelle Shocked’s *Anchorage, Alaska * always gets me.
The Bonnie Prince can draw the tears. The whole ‘I see a darkness’ album is black - ‘today was another day full of dread’, ‘death to everyone’ and the title track really get me emotional. I’ve seen him play ‘I see a darkness’ live and folk have been crying.
At the other end of the cheese spectrum, there was a track popular in the US when I was there a few years back from a soft rock outfit, had a refrain like ‘Angel closes her eyes’. Bit of a tear-jerker to be honest.
Do you mean “Lightning Crashes” by Live? (http://www.youtube.com/watch?v=SQbAz-cgDR8) Not really a soft rock outfit if so; they’re fairly hard rock alternative usually. 
Oh, and I forgot Alyssa Lies, by Jason Michael Carroll. A gut-wrencher, that one.
In addition to the Country Songs already mentioned, Concrete Angel by Martina McBride and The Little Girl by John Michael Montgomery get me every time.