Normally I hate doing covers, but I've done a few over the years:
Failure - Smoking Umbrellas (awesome)
Alice in Chains - What The Hell Have I (sucked)
Depeche Mode - Behind the Wheel (we made it sound like Sabbath, and therefore awesome)
R.E.M. - Losing My Religion (bass/drums/vox only, and last we did this I fucked up the ending mandolin bit amazingly so)
Beatles - She's So Heavy (another Sabbath sounding one, although it already does that originally)
Nirvana - Breed (first fuzz use in a band awwww)
Ween - She's Your Baby (I hate this band, but I get why my guitarist likes them)
I think that's it, at least performance wise. Oh and a few years ago I recorded The X-Files Theme on bass:
[soundcloud]http://soundcloud.com/adrian_smith/the-x-files-theme[/soundcloud]
I tried to get an old band of mine to do New Dawn Fades by Joy Division but they wouldn't. Fuckers.

Also I started to learn Moonlight Drive by the Doors, doing the entire keyboard part on bass with whacky harmonics and shit, and that was awesome/hard, but I quit the band before we could finalize it. Alas!