How Slammer spread so fast

A group of researchers are already out with a paper detailing the rapid spread of the Slammer worm (also known as Sapphire):

Sapphire's spreading strategy is based on random scanning -- it selects IP addresses at random to infect, eventually finding all susceptible hosts. Random scanning worms initially spread exponentially rapidly, but the rapid infection of new hosts becomes less effective as the worm spends more effort retrying addresses that are either already infected or immune.