It would be tough to sell "digital items" for an avatar when it's an image of a user. Both Facebook and Myspace allow you to choose whatever image you like, but it's generally accepted that you select a portrait of yourself. I suppose there are some ideas out there to "customize" your profile and that may work.

Games do seem to work, but no one buys them online when most are free - so mobile seems to be the only way to make that happen. I agree with the comment that it sounds like the iPhone App store. That technique is definitely working, but there have to be better alternatives to monetize these sites.