Anything by William Shatner.

Cat Power "Sings Dylan"

Trout Mask Replica, Captain Beefheart.

Thanks for all the albums.  Deadicated is excellent. 

Deadicated: A Tribute to the Grateful Dead

Siouxie and The Banshees - Through the Looking Glass

+1 If I Were A Carpenter - My favorite track is Sonic Youth’s cover of “Superstar”.

Another good cover album has various artists covering the music of Richard and Karen Carpenter.  The album is called "If I were a Carpenter."  I particularly like Shonen Knife's version of "top of the World" and Redd Kross' version of "Yesterday Once More."

I particularly like the French duo who goes by the name Nouvelle Vague.  There self-titled album is particularly good.  They primarily cover Brit Pop.

For the really outrageous, so bad it is interesting, I suggest:

Pat Boone (Christian music) doing weird jazz band covers of heavy metal, the album is called "No More Mr. Nice Guy" (he is wearing leather on the cover art).

How about "Sebastian Cabot, Actor/Bob Dylan, Poet" (the actor does a dramatic reading of Dylan lyrics while truly awful versions of Dylan's music plays in the background.

For individual tracks, check out Klaus Nomi: "Just One Look"

https://www.youtube.com/watch?v=2yplwTe5IFQ

And then there is Yoko Ono doing Adele:

https://www.youtube.com/watch?v=ZsgMbxyDmCY

Lucinda Williams/from Lu's Jukebox, A Tribute to the Rolling Stones, Funny how time slips away/a night of 60s country songs, Bob's Back Pages/a night of Bob Dylan, Southern Soul/From Memphis to Mussel Shoals, and finally Running Down a Dream/a tribute to Tom Petty. Enjoy the music

Sinatra Sings the Beatles!

Sharp Dressed men / A Country Tribute to ZZ Top, Please take note of Alan Jacksons cover of, Sure Got Cold After The Rain Fell, he tears it up on 2 levels. Enjoy the music

"Pinups" David Bowie

"Wallflower" Diana Krall

"The Birds Play Dylan" The Byrds

Foreverly by Nora Jones and Billie Joe Armstrong covering the Everly Brothers album, Songs Our Daddy Taught Us. Enjoy the music

Wow, so many to list but will suggest a few. Come on up to the house / Women Sing Waits, Dwight Yoakam / Dwight sings Buck, Steve Earle /  Townes, Steve Earle / Guy, The Art of McCartney / various artist singing Paul McCartney songs and I could go on but.....Enjoy the music

Sweet Home Alabama: The Country Music Tribute To Lynyrd Skynyrd