This is pretty easy for me.
My favorite Dylan covers were done by the Byrds. They had a whole bunch of 'em.
I'm pretty sick of this version, but I used to really dig Hendrix' take on "Along Along the Watchtower".
Sundog, if you like "If Not For You", you need to track down a bootleg of the 1970 Dylan/Harrison sessions. I believe they cowrote that track together.
I know it's not a version by another artist, but I LOVE Dylan's version of "Tonight I'll Be Staying Here With You " from the LIVE 1975 (The Bootleg Series Volume 5) CD. The original track was on NASHVILLE SKYLINE, but it might as well have been a different song.