Give a service away for free, possibly but not neccesarily run ads, acquire a lot of customers very efficiently through word of mouth, referral networks, organic search marketing, then offer premium priced value added services or an enhanced version of your service to your customer base.
Examples:
Skype - basic in network voice is free, out of network calling is a premium service
Flickr - a handful of pictures a month is free, heavy users convert to Pro
Trillian - the basic service is free, but there is paid version that is full featured
Newsgator - the web reader is free. If you want to synch with outlook and your mobile phone, that's a paid service
Box.net - you get 1gb of virtual storage for free, but you have to pay for more than that
Webroot - you can get a free spyware scan, but for full protection you need to pay
This business model has been around for a long time and is used a lot by todays web 2.0 companies.
It works best with web native services. A customer is one click away and if you can convert them without forcing them into a price/value decision you can build a customer base fairly rapidly and efficiently. This means simple initial customer acquisition process. Asking for a credit card when nothing has to be charged is not a good idea and forced registration neither. You'll want these things after building trust and not in the initial interaction.
The best examples of this business model are when the customer implicitly understands why the paid service has to cost money. More storage costs for photos or virtual storage are good examples. Termination costs on other carriers networks in the Skype model are another. When it is just additional features that don't carry an incremental cost to offer, it may be harder to convert free users to paid users. But if your free service is loved and you do a good job articulating the value that comes with the paid service, you can convert to paying users with good results.