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.
the Gourd’s cover of Gin and Juice by Snoop Dogg
(Apparently many people thought it was Phish who performed this cover, it was shared and torrented a lot as a Phish cover)
Puts me in mind of Ben Folds’ version of Bitches Ain’t Shit.