My last post notwithstanding, I would say since U2 and R.E.M. can't be considered a *current* pick for greatest band, I would have to say The White Stripes, not for being my favorite band (they're not) but for being a great band that is popular enough to vie for a 'greatest' label (and of course for being a band, as opposed to a solo singer or 'group'). The other reason I pick TWS is because they're current, i.e. still in that maximum creativity zone (I hope.)
Radiohead is a contender but its been, what 3 years since Hail to the Thief? And listening to Hail to the Thief I wasn't thinking greatest current band at all, I would have considered it during the releases of 'The Bends' and possibly 'OK Computer'.
Here's an observation - since some of the listed bands had their heydey in the mid 90s, Oasis is a band that almost everyone is really sick of now, but had this question was asked in late 1995, I bet there would have been some Oasis nominations in a thread like this, even over Radiohead, despite that being the release period of The Bends. Of course not too many people will admit that now.
Edit: Oops, re-reading this thread I see Oasis listed previously. Of course, I don't think they fit because they certainly aren't a current band, unless they've re-united?