I'd make the case that Radiohead was the band of the millennium's first decade. Four critically glorified albums, stadium tours, the works. While they ain't exactly "indie", I think that like Beck, The White Stripes, and a few others, they've gone mainstream and yet managed to maintain a high level of indie cred (currency about as valuable as used toilet paper, but something to strive for nonetheless.)
At any rate, they dominated the decade like few others. My Morning Jacket could be in the discussion: They've earned top billing for festivals and released steadily praised music with few missteps. Wilco too.
But for now, let's gaze into our crystal balls (hee): Who will be the biggest band of the oughts? Let your voice be heard, or email us if you think we missed a choice.