Ryan Adams' Wonderwall is one of my favourite covers. He basically did for that song what Jeff Buckley did for Hallelujah, stripped it right back to its gorgeous skeleton.
Maybe it goes without saying, but generally, "every Dylan song" is just the view of people who don't like him in the first place (as are a good majority of "I prefer the cover"s overall). Coming from someone who does like him, I think very few of his covers stand up to the originals. Guns n Roses' Knockin' on Heaven's Door is about the most heartless, ridiculous, over the top take on that song I could possibly imagine. Having said that, I can't stand GnR, so go figure. And either way, The Grateful Dead have various versions that absolutely destroy anyone else's take, like
https://archive.org/details/gd78-11-17.acoustic.sbd.dodd.7687.sbeok.shnf (acoustic) or
https://grooveshark.com/#!/s/Knockin+On+Heaven+s+Door/2h7qim?src=5 (electric)
The best Dylan cover I've ever heard is Rage Against the Machine's version of Maggie's Farm.
Stevie Ray Vaughan managed to improve Little Wing (though I don't care too much for the original Little Wing), and probably Voodoo Chile (Slight Return) too.
Jeff Buckley has tons of awesome covers. Off the top of my head, I love his Strange Fruit, Dink's Song, and Je Ne Connais Pas Le Fin.
Mingus Big Band's version of Moanin' gives the original a run for its money.
There's a New Zealand reggae band called Katchafire (they started out as a Bob Marley tribute) that do an incredible Redemption Song.
Metallica covers don't get any better than Am I Evil?
I think I prefer Tool's version of No Quarter.
And an assorted bunch of others:
Nirvana - Man Who Sold the World
Pearl Jam - Last Kiss
Phish - Peaches en Regalia
Animals - House of the Rising Sun
Faith No More - Easy