For subgenres, The Beach Boys took “Chapel of Love” from Motown to Surf. I actually prefer their version.
Boston ska band Bim Skala Bim did a ska version of Pink Floyd’s “Brain Damage” (“The lunatic is on the grass…”)
I think you can hear it here: BiB Records - (Bones)
More than one album - he’s also released “Apertif For Destruction”, “I’d Like A Virgin”, and “Tuxicity”.
All of which, sadly, I own. 
New Grass Revival did a bluegrass version of Marvin Gaye’s *Ain’t That Peculiar. *
It worked.
Dar Williams covers “Comfortably Numb” and turns it into a folky sounding song.
Any of Senor Coconut’s Kraftwerk covers.
19,752 covers of “Memory” that sing it like a dirge.
It’s suppose to be a reflective song.
Joe Piscopo’s homage(?) to Frank Sinatra on the medley, “I Love Rock 'n Roll”
Eva Cassidy’s “Time After Time.” Very not a 70’s pop song.
I love rock n roll - Britney Spears (rock to rubbish)
Alanis Morrissette - “My Humps” (rap to slow ballad)
Celldweller - “Tragedy” (Bee Gees disco to industrial/EBM)
Thanks for the reminder, Quercus. They also did an outstanding cover of The Who’s Shakin’ All Over.
Reel Big Fish - Hungry Like the Wolf
Jimi Hendrix took the National Anthem electric at Woodstock.
Blue Cheer went acid rock on “Summertime Blues”
And who could ever forget Donna Summer’s disco turn on “MacArthur Park”
“I Will Survive” by Cake–I don’t know what genre you would call it, but it isn’t disco.
I had no idea that the sweet, country-folkish song Alison Krauss sang, “Baby, Now That I’ve Found You” was originally a soul song with horns.
Or maybe not–it seems The Foundations also recorded it, but I’ve never heard that version.
There is a collaborative band called Nouvelle Vague that quite specifically does genre shifts of 80s music. For example, the swing version of “Dancing with Myself” used in this YouTube thing and goofy samba version, or bossa nova of other songs by Echo and the Bunnymen, the Clash, Lords of the New Church, Depeche Mode, etc.
They are best known for this version of “Just can’t Get Enough” by Depeche Mode which was used in a car commercial.
We actually really like their CDs they are really fun. I particularly like their version of Bauhaus’s “Bela Legosi’s Dead”.
Ray Charles cover of Ring of Fire. From country to fucking awesome.
I’m a fan of Grey DeLisle’s country version of Bohemian Rhapsody!
Well there’s everything Richard Cheese has ever done(eg. “Down with the sickness” in Dawn of the Dead), but I’m not sure if he should count since changing songs to lounge music is his entire gimmick.