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. Thanks to everyone for all 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 it I stayed up a bit too late a number of times.

Worth it.