Hendrix-All Along the Watchtower (Dylan)
Nouvelle Vague-Guns of Brixton (Clash)
Shonen Knife-Top of the World (Carpenters)
Odetta-Times They Are a Changin' (Dylan)
Orbison, Nazareth-Love Hurts (Everly Brothers)
Be Good Tanyas-Waiting Around to Die (Townes Van Zandt)
My Chemical Romance-Desolation Row (Dylan)
I also like the Cowboy Junkies cover of Thunder Road and the Dread Zeppelin covers mentioned above (I particularly like the mashup of Zeppelin's Heartbreaker and Elvis' Heartbreak Hotel).
For so aweful, it is inspiring:
Sebastian Cabot reciting Dylan songs (e.g., It Ain't Me Babe)
Bob Dylan and Tiny Tim doing Sonny and Cher's "I've Got You Babe"
Captain Kirk doing "Mr. Tambourine Man" and "Lucy in the Sky with Diamonds"
Mae West doing "Twist and Shout," which is itself, a cover/ripoff of "La Bamba"