The Big Push -- Praise You (Fatboy Slim):
They are at their best when they glide through various songs creating something new but yes, I think "Praise You" is their most interesting full cover:I like what they did there. And the fact that the song itself is samples/covers of about 9 different songs. (including "Take Yo Praise", Disney's "It's A Small World", and Fat Albert and the Cosby Kids "Gonna Have A Good Time")
This song started my lifelong love affair with Bonnie Raitt’s music
Post Modern Jukebox (Scott Bradlee) does all kinds of crazy covers (changes up genres). Here's one I like quite a bit.
U2's "I Still Haven't Found What I'm Looking For". Featuring Rogelio Douglas Jr.
There have been many covers of this Neil Young tune. This is one of my favorites.