Songs which transcend covers

There's a music video thread, a novella thread, so I thought I'd start another thread with songs that move you no matter who sings them.

Leonard Cohen's "Hallelujah" is on the top of my list. I can't think of any other song that has been covered so well by so many people. I think Jeff Buckley's version is the best, but I'm also including kd lang's, because I just heard it and it is incredible.

For those of you who don't know, Buckley died in 1994 at the age of 30, after recording his album Grace, on which "Hallelujah" was a track. He actually recorded 20 different takes of the song, and the final track was mixed from 3 of them.

Here's Buckley's studio version (click HQ to watch in High Quality, otherwise it won't work):




Here's kd lang's (yes, her name is in lower case) live version at the Canadian Juno Awards:



Do you know any other songs that are as universal as this, or just have really good covers? Ironically, Cohen's original sounds very very different from these covers.

EDIT: Forgot to add that Kate Voegele's version of this song is absolutely horrific. I didn't post it here, but maybe I should have, so that you can appreciate just how good Buckley's and lang's versions are.

I love Alexandra Burke's version of Hallelujah