Invincible Cydonian Creep
*cough* Radiohead *cough*
*waits to be hurt*
If you hadn't said it, I would've.
It depends, no band sounds like them altogether. But there are some that are similar in certain ways.
Tom Morello (Rage Against the Machine) was a big influence on Matt's playing, so there are a few similarities in the guitars there.
Vocally (And the mixing/production on Showbiz), Radiohead.
The piano/keys work borrows heavily from Rachmaninov, sometimes Matt just out-and-out steals from him.
I'm sure there are many others, but I'm not very broad in what I listen to.