Jay Meattle of the web statistics firm compete has done an interesting analysis of the growth rates of MySpace vs YouTube. He concludes that YouTube's rate of growth exceeds that of MySpace - i.e. essentially it is more viral!.
It took YouTube 16 months to reach 20 million users, but it took MySpace 25 months. So YouTube was nine months quicker to reach that 20 million users mark.
Jay speculates that if YouTube's growth continues at this rate, then it will break 50 million users within 12 months - making it among the top 10 websites in the world. Of course, YouTube was also nearly 3 times as expensive as MySpace (Google paid $1.65B compared to News Corp paying $580M for MySpace last year). So Google has paid a premium for that fast growth!
It could also be that YouTube's growth was helped by the growth of the Web market in general - i.e. YouTube came after MySpace, so they took advantage of higher growth rates in the Web market. In any case, YouTube's growth has been phenomenal however you look at it. Will we see another big website with that rate of growth in this era? It's doubtful.