Aztec Camera: Jump (originally by Van Halen)
This is the first song I can remember in this genre. It's still one of my favorites.
Mat Weddle: Hey Ya (originally by Outkast)
Nice acoustic version of a song I like.
Travis: Baby One More Time (originally by Britney Spears)
Nice acoustic version of a song I can't stand.
Gary Jules: Mad World (originally by Tears for Fears)
Cool video for this one. I like the soul he puts into this song.
A Thousand Miles From New York (three guys on a bed): Santeria (originally by Sublime) and Killing Me Softly (originally by Roberta Flack)
I want to party with these guys! Seriously. I want them to jam in my basement. I will supply all the beverages and munchies they want.
Note that I have not included the particular sub-genres of jazz covers of rock songs (The Bad Plus do a great job of this) or lounge versions of songs (a la Richard Cheese and Lounge Against the Machine who rock in an incredibly groovy way).