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.
Two very different examples:
Modest Mussorsky’s “Pictures at an exhibition” was originally written for piano (that was all the poor guy had available), and it took Maurice Ravel to turn it into an orchestral version and make it popular world wide. Both versions are great and have their own qualities, but I far prefer Ravel’s version (Although Khatia Buniatishvili’s rendition here is so really really good).
Bob Dylan’s “Lay Lady Lay”. The original is… well… it’s a Bob Dylan song. There is a really good cover version by Ministry that, althought technically is the same song, takes it to a whole other level. Love it.