A number of Web 2.0 businesses are not started with clear business models in mind. MySpace is a classic example - the founders started it as a way to share music within their personal networks, never anticipated it would become the phenomenon it has, and consequently now struggle to find the right business model that will bring in the level of revenue you might expect from a site with such extraordinary levels of traffic and stickiness, while not compromising the reasons why the users love the site.
Broadly speaking, the most prevalent Web 2.0 business model is 'if we start a site, offer what it does for free to the public at large, and bring in lots of people that way, then we'll be able to charge advertisers to advertise on it and make money that way' OR 'we'll be able to sell it for a large amount of money to someone else who can figure out how to make money from it'.
Web business models for 'that's a neat idea!', as opposed to web ventures that are based on traditional business models (retail, subscription), are tricky. The nature of the web is that people expect to get things for free, and so many web ventures presume that they cannot charge for what they do, and their only recourse when it comes to making money is an ad-supported model.
However, some of the fundamental principles that operate in the offline world also operate online. People will pay for something they consider to be of real value to them. The optimal web business model enables a badly-needed solution to a problem, is therefore able to charge for and profit from what it delivers, does so in a way that engages and inspires loyalty in its customers, and thus is able to commercially partner with other entities who need to find a way of reaching those same customers.