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
EDIT: This has been great, everyone. Thank you all for the terrific links and for introducing me to a number of artists I wouldn’t have heard of otherwise. Seriously, the online rabbit-holes have been thoroughly enjoyable–even if I stayed up a bit too late a number of times.
Worth it.
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.
I once got to see The Easy Star All Stars playing Dub Side, and it was magnificent. Such a great band.