Love it! 
Apparently Mick recorded the demo version himself, so there has been a lot of talk that it's really just a Mick song. Also, apparently the YouTube version is a "radio edit" version and there is a version on iTunes that is supposed to be the album version and is considerably different.
Taken from Wikipedia:
The song's opening riff is played by Mick Jagger. Richards commented on Jagger being the driving force behind the song and Jagger playing the opening riff: "I don't give a damn. He'd never have learned how to play that without me teaching him how to do it." 
http://en.wikipedia.org/wiki/Doom_and_Gloom