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
Did anyone already mention Johnny Cash’s version of Hurt, original by Nine Inch Nails? A marvelous reimagined version, maybe, the best cover ever.
Hurt - Johnny Cash