David Byrne singing “These Boots Are Made for Walkin’” and “I Wanna Dance with Somebody.”
My favorite is Ben Folds covering “Bitches Ain’t Shit” (Dr. Dre).
Cowboy Junkies’ version of “Sweet Jane”?
(This one is particularly interesting as the original Velvet Underground version was relatively soft, then came Lou Reed’s hard live version, then the Junkies’ almost catatonic cover.)
Local H has a version as well.
Pure awesome.
I’m not sure this counts but theres something haunting about Bruce Springsteen’s acoustic Born in the USA
…and sexy about Nelly Fertato’s version of Gnarls Barkley’s Crazy
Here’s the Cowboy Junkies: http://www.youtube.com/watch?v=BHRFZFmEq9o
But this isn’t a novelty cover like some of the others.
I believe that cover was done by the Gourds, not Phish (as it’s commonly wrongly attributed to).
The wonderful Red House Painters did a cover of Kiss’s “Shock Me”. It’s not funny or ironic, but it actually turns it into a beautiful song.
I have Zwan/Billy Corgan’s soft and creepy cover of Iron Maiden’s The Number of the Beast.
Not that the original was all that “hard,” but Daughtry’s Poker Face is actually listenable. Unlike the Lady Gaga original.
I just love this version of Don’t cha by the Baseballs.
(Original for those who would like quick comparison 
http://www.youtube.com/watch?v=z4XgP5tnI4c&feature=fvw ).
Which may have inspired Dion to cover Purple Haze a few months later.
I’ve got that Pat Boone album and it’s wonderful. He also does Enter Sandman, Smoke On the Water, Paradise City and Stairway to Heaven, all in a Rat Pack/Nelson Riddle style with big band arrangements and a trio of female backing singers. Worth $13.98 of anybody’s money.
More details here:
Ray Lamontagne did a good version of “Crazy” too: http://www.youtube.com/watch?v=6mEfDSP4g_U
Huh. Waddaya know.
Ignorance fought (and MP3 renamed). 
Mad World by Tears for Fears, is not exactly a hard song, but it is quicker and “dancier” than the slower more emotional version by Gary Jules and Michael Andrews.
Its not particularly ironical.
I thought David Cook’s rendition of Billie Jean was amazing.
Sissy Bar’s cover of Gin & Juice
Very interesting, but doesn’t sound like '70s funk at all to me. I was imagining something like “Brick House” or a P-Funk track. This is more like an Amy Winehouse ‘neo-soul’ kind of thing.
There are a couple of slow, mellow versions of the theme to the old TV show Hawaii Five-O, my favorite of which is the Blue Hawaiians’ Martini Five-O.
Great surf instrumental.