The Doors were amazing, and they did not have a regular bass player. Ray Manzarek covered the bottom end with his keyboards.
Emerson Lake & Palmer have many tunes in which Greg Lake takes a guitar solo, and when they play it live, Emerson covers the bottom end with keyboards.
For that matter, last time we rehearsed, our bass player was half an hour late, so I covered the bottom end on keys (anyone see a pattern?) and our WL turned around a started looking for our bassist, assuming he'd slipped in the back way or something. Nope, just me.
There's no question that a good bass player adds a lot to the sound of a band, but it is not required. But I can't think of any rock band that doesn't have something in the lower end. It just seems like you'd need it. I've never listened to White Stripes, so I didn't even know that they don't have a bassist. Probably too busy checking out the girl with the big breasts.