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.
YoVille! PetSociety and more all make money selling virtual currency to buy in-game objects. If transferring money from fb into an fb app were painless and had cheap txn costs, two things would happen. 1) More people would spend! Frictionless, and with the authority of Facebook, an integrated payment solution would help separate people from their money and 2) a LOT more developers would get in on the action.
PayMo charges 5% for cellphone txns, but the carriers charge up to 50%. That is totally outrageous. Games are some of the biggest apps on Facebook, and this would be a good way for facebook to make money, and encourage/help their platform developers.
Disclaimer: These are my opinions and not those of my employer, FooMojo, Inc (creators of FooPets on Facebook.)
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.