Not to be outdone...
I was so inspired by the Ryan Adams cover that I thought I'd post my two favorite Dylan covers. Most Dylanologists would take great exception to me not putting in the Jimi Hendrix cover of Along The Watchtower, but whatever. Both these songs are really really really good.
Eddie Vedder - Masters of War
This is unquestionably beautiful. Vedder's voice winds his way through Dylan's lyrics and the background is even more minimal than the original. Fantastic.
Guns & Roses - Knockin' On Heaven's Door
They couldn't have made this song more late 80s. Huge snare. Weird phone dialing interlude. 5 part dubbed harmonies. Guitar slides. Piano riffs. It turned Dylan's funeral opus into a glam rock masterpiece of sorts. But HOLY SHIT! This song was made for Axl Rose to croon. It works so well it should be a crime.