The Danish NemID ("easy ID") uses the Danish SSN, a password and strike list for login to the many government services (you can get divorced online if both parties agree ), banks, contracts (e.g. signing deeds to a house), gambling where you need proof of age or other proofs of identity (e.g. you can validate yourself on the eBay/craigslist equivalent to make your buying/selling more credible).
NemID itself is ran by a private party -- the basic pricing is 50 cents per unique user or 15 cents per session if you are a non-government entity.
There are some privacy protections -- as non-government entity you cannot get to the SSN, just another ID, but you can ask the user to enter their SSN and verify it's valid for that user.
It's working pretty well after they finally got rid of the Java encryption applets. However you need to have a Danish SSN to use it, so you either live in DK or are a citizen.