Originally Posted by askrom
I always assumed this had something to do with the harmonics of the bike, that some vibration is in "tune" with the bike and thus the effect only increases. I've noticed this effect is massive when my city cruiser bike has a large rack on the seatpost but nearly non-existent when the rack is removed. Something about the top-heaviness, maybe, but it feels a lot like a harmonic effect and the effect seems to be bike-wide, not just in the wheel.
The whole bike is indeed involved because of the steering effect of the wobble. Jobst Brandt described it in terms of bicycle dynamics, I suspect that it's when the two undamped systems (ie the bike and the wheel) match frequencies that things are set off.