I'd like to see Shiina Ringo/Tokyo Jihen try covering some Radiohead and Smashing Pumpkins, a couple of my favorite bands. Modest Mouse is another possibility. Getting even more obscure here, Porcupine Tree is another band that I have wild fantasies of Tokyo Jihen trying. >_>
I know she did Creep, which was alright, but Creep isn't really that great of a song to begin with. One of Radiohead's weakest.
Some Radiohead songs I think SR/TJ could try to do:
"You"
"My Iron Lung"
"Paranoid Android" (that would DEFINITELY be wild)
"Electioneering"
Some of Shiina's early work really had a grungy sound and reminded me of the Smashing Pumpkins at times. Here's some songs that I think could work...
"Today"
"Tonight, Tonight" (would be really interesting if TJ could pull off a unique rendition)
As for Modest Mouse...
"A Different City"
"The Stars are Projectors"
and finally Porcupine Tree:
"Blackest Eyes"
Perhaps my tastes are a bit eclectic, but I've barely scratched the surface.
I could go on and on...A Perfect Circle, Weezer, Beatles, Ben Folds, Jimmy Eat World, etc...I think I'll stop now.