Don't forget Shatner's "Mr. Tambourine Man," another amazing cover. This, and a bunch of other aweful covers can be found on a CD called "Golden Throats." That album included Sebastian Cabot doing "It Ain't Me Babe). That cover prompted me to find the original vinyl which is a whole album of him reciting the lyrics to Bob Dylan songs to a musical accompaniment.
Another album worth hunting down, is "No More Mr. Nice Guy"--Pat Boone doing covers of heavy metal hits in a sort of big band style.
I don't know if "covers" include someone singing standards, but my all time favorite tasteless, crazy, brilliant and wonderful cover is Jackie Wilson singing "Danny Boy."
Another cover that has some cheesy parts, but is utterly amazing and wonderful--so it is bad and it is good at the same time--is Lester Bowie (jazz trumpeter) doing "The Great Pretender."