It’s John Cale’s version that Jeff Buckley covered, and for me it’s between those two (even though I love Cohen, his version’s a bit tossed off).
I’d have to go for Cale’s, because there’s less of the vocal gymnastics, and his voice suits the words far better than Buckley’s. Try to hear the version on his Fragments of a Rainy Season live solo album.
Buckley Buckley Buckley
Buckley
The score so far:
Buckley 5
Wainwright 3
Cane 3
Cohen 2
A vote for Buckley.
His guitar arrangement on it adds a layer, and that last note that he holds forever cuts me to the quick.
But my favorite part of his version is how is starts it off with that lamentable sigh. He sounds tortured before he even sings a note.
Great. What are you guys saying here? My sister has better taste in music than me? WHY I AUGHTA…
I dug up copies of the Cohen version, the Buckley version, and the Wainwright version this afternoon to see which one I liked best.
Rufus Wainwright is definitely tops on my list, but I like Jeff Buckley’s version too. Very different from Rufus, but nice. (I would rather like to hear more of his music, I think.)
Jess:
Go buy his Grace CD. It is one of the best albums in the history of recorded music. 
And no one mentioned Bono’s version but me… not that I really enjoyed it… I just find it curious.
John Cale… sigh
Another Buckley fan here. That “huhhhhhh” intake of breath before the first note is played gets me.
How about another (sub) game? Name scenes in movies and on television where the song is used. We have the Shrek example, above. Another one is in The West Wing, when CJ roams the streets in the rain after her bodyguard is shot.
I’m sorry but if you haven’t heard Cohen’s orginal version, you are disquailfied from voting (even if you wrote the OP).
That said, I think Cale edges out even Cohen.
(Sorry, I like Rufus quite a bit but he doesn’t come close here.)
Narrad The Cale rendition was also featured in Basquiat IIRC.
Jar, I do like the Rufus version better than the Jeff version if that helps. 
Rufus Wainwright by a mile. I had to come in just to cancel out Jack Batty’s vote.
RUFUS.
I have copies of all except the Bono one, which I have heard before. And the winner is…
Jeff Buckley. He lived and died that song. Absolutely beautiful. No one could impart more emotion into that song than him.
I love John Cale, but his version just doesn’t do it for me. I also agree with ** HenrySpencer ** that Cohen’s version sounds tossed of. I like Rufus alright, but his “Hallelujah” doesn’t have the true emotional weight the others have. A bit too overwrought for my taste, or something.
Leonard Cohen. Nuff said.
My votes go to Wainwright and Cohen.
I HATE Bono’s version of the song.
Oh, and jar, if you want a good Cohen song, try “Take This Waltz.” Romantic and a little heart-breaking too.
Yeah, I’m not sure the dance beats worked well with it…
Leonard Cohen wrote and recorded the song.
Others have since tried to remake it.
IMO, they have failed:)
Cohen by a league and a half.
Rufus. Rufus, a million times Rufus. I like Buckley’s version, but I prefer Rufus’s deeper voice.
The Cohen version I have is him basically chanting the lyrics. Weird.
Absolutely. there is no question about it.
although John Cale’s version isn’t too bad…