Zuckerberg is most definitely NOT a genius. When Facebook first came out in 2004, the reason it became so popular was the apparent exclusivity for college students; nobody else could register.
Once it took off and he got a lot of VC funding, in 2004-2005, he slowly started opening it up and eventually people were drawn to it for reasons some have already stated (looked better than MySpace etc.).
The reason Facebook took off after 3-4 years are threefold:
1.) Facebook is a social network that doubles as a dating site without the stigma of one.
2.) Facebook enabled (still does) people to get in touch with folks whom they hadn't seen or talked to in years, in some cases, decades! For example, I reconnected with two of my friends from 1st grade on Facebook!
Facebook also gives you the ability to vicariously involve yourself in others' lives. Back in the day, you had to make an effort to rekindle relationships with friends. Nowadays, all it takes is a silly "Wall" post. In other words, the ability to befriend others and rekindle relationships without committing oneself as one would have to do in real life gives tremendous satisfaction to many.
3.) The most "genius" thing that Facebook did, and I would guess that it was not just Zuckerberg who came up with this, was the "app" phenomenon.
Facebook singlehandedly started the "application development" phenomenon on a public site. Until then, consumers were at the mercy of the corporations/companies that decided to add certain key functionality into the sites. After the introduction of Facebook Apps in 2007, developers from around the world were able to create various programs that people could use of their own volition. This, indeed, was a stroke of genius!
After this Facebook App phenomenon, every major corporation in software jumped on this bandwagon (Apple's App Store came afterwards) and now, applications are commonplace. Facebook singlehandedly changed the marketplace for functionality and interaction between users, developers (big & small), and publishers.
Once this Facebook App phenomenon took place, Facebook never looked back. Their user-base increased exponentially and now they have the Internet in the palm of their hands; even Google is spooked by them. Each "profile" on Facebook is worth a LOT of money to the advertisers. They can and will use them, however surreptitiously, to market to big corporations and make billions of dollars.
Facebook's success is definitely shared among their employees from top to bottom and Zuckerberg does deserve a lot of credit. Yet, to call him a genius is a disservice to other true geniuses like physicists, mathematicians, economists, and philosophers whose genius was not guided predominantly by luck, but by perseverance, hard work, and a proclivity for cognitive reverie.