Free, like a Metro newspaper
No surprise, free newspapers that you can pickup in the subway or around town are advertising supported. The "money flow" in the business (advertisers paying publishers) is disconnected from the customer base (the readers). More readers does indeed boost advertising revenue, but there's no effort in this model to extract cash from readers.
Free, like Twitter
Many internet companies offer free services, such as Twitter and Facebook. In addition to advertising (like the example above) these companies are looking to leverage their audiences by charging businesses for use or exposure to that audience. Again, the customer base is not being asked to pony up cash. (and this isn't to say that these guys won't go the Freemium route later, or that they have no business model).
Free, as in Freemium
Free in this model is used as a "tasting" that leads to a portion of the userbase upgrading to the premium version. This is one way that LinkedIn makes money. They offer a great service that needs lots of users to sign-up in order for their model to work (which is another reason to offer a free service - their model wouldn't be too useful if there was no one in your professional network) and a portion of the users pay for their premium offering.
So, if you're thinking about applying a marketer's favorite word ("Free") to your business model, make sure you have a clear understanding of the different versions and implications of free business models.