I have only three versions (although the thought of an Imogen Heap version has sent me off to search for that too). I first heard the Jeff Buckley version when a friend of mine lent me the album Grace, and since then I picked up the Cohen and the Rufus Wainwright (which I also heard him sing live in concert and made me cry).
I don't actually think I prefer one version or another, to be honest. It really depends on the mood I'm trying to set.
Speaking of Leonard Cohen, I don't know if you've heard this, but the other song of his that grabbed me recently was 'A Thousand Kisses Deep' (which I heard on an episode of Veronica Mars, oddly enough). I handed it off to rosamund and she turned it into an absolutely devastating piece of writing.