So what makes someone on Facebook, or Twitter or My Space cool? This is a legitimate question. I don't subscribe to any of those "social networking" services, so i really don't know what people do to establish their "cool" online.
Pretty much the same things as in the brick-and-mortar world. If you look at the most popular folks on these sites they are usually popular (with some very notable exceptions I'll explain below) off the internet as well.
Here's an example from the most followed twitter users:
1) Ashton Kutcher
3) Britney Spears
4) TheEllenShow (Oprah just joined this month, she can outdo this if she wants)
5) Twitter (of course)
7) Jimmy Fallon
9) John Mayer
10) Demi Moore
As you can see, the top ten most popular twitter users did not become popular on twitter itself.
Now as to the exceptions, there are a class of "online celebrities" who are famous just on the internet. These tend to fall into three main categories:
1) People who control a lot of traffic and used the traffic to establish a following. E.g. founders of famous sites, blogs who leverage their existing readership to become friends and fans.
2) People who work for companies as their customer representatives. E.g. Any Google employee can be popular online, they just have to start answering questions about Google and they'll have a legion of followers.
3) Genuinely clever and informative people. Some folk really do get by on the strength of their own contributions alone. They don't tend to be more popular than the above two categories, and the above two often are where they are because they too make useful contributions (not always) but some don't really self promote and have a loyal following.