Here are a few to get things started:
Don Henley’s The Boys of Summer as an 80s synth tune
Bossa nova version of Crowded House’s Don’t Dream It’s Over
Reggae-ish version of Aretha Franklin’s Respect
A capella men’s ensemble version of Lady Gaga’s Bad Romance
Dub Side of the Moon, a reggae cover of Dark Side of the Moon. https://en.wikipedia.org/wiki/Dub_Side_of_the_Moon
Joke answer: Disturbed’s “The Sound of Science” cover because it’s fucking horrid and ruins the point of the original’s meaning.
They also did OK Computer (Radiodread); their cover of Let Down is one of my favorite covers all-time.
I once got to see The Easy Star All Stars playing Dub Side, and it was magnificent. Such a great band.