The wierdist cover I've heard has to be 'Under Pressure' by Keane and it was originially by David Bowie/Queen. First I hated it, now I kinda like it. The cover is excellent, they improved the vocals and sound, it's just that the actual song is sorta wierd. Anyways, you can judge:
http://youtube.com/watch?v=AEhUcRv0iO0
And the Kooks (fairly new English band) did a good acoustic cover of Crazy where they play it along the streets of some French city.