Well, some consider these great new "interpretations," but although I like the singers, I consider these more "butcherings" of the original songs than mere new "versions":
Eva Cassidy - Over The Rainbow
Bruddah Iz - Over The Rainbow (again)

And I say that because both of them almost totally lost/destroyed the song's melody (plus Iz butchered the lyrics too).

One I don't think is "awful" but IMO can't hold a candle to the way the songwriter herself sings it is Counting Crows' "Big Yellow Taxi."

Then there's UB40's reggae version of Elvis's "(I) Can't Help Falling In Love (With You)." For one thing, he changes the line "Like a river flows surely to the sea, darling, so it goes; Some things are meant to be" to "... flows gently to the sea .." - thus destroying the simile.

One more gawdawful rendition of a song - DK if you could call it a "cover - is Patsy Cline's lounge-singer style rendition of "Life's Mountain Railway."   It's so bad it's actually funny.