You could use ACS (Access Control Service, part of Windows Azure Active Directory). That would let users interact with social providers like Facebook, Google, Windows Live, and Yahoo!
If you need to interact with a database, you could alway go with an ASP.NET membership provider that stores data in SQL Database. This is basically the same as you'd do it with an on-premises solution.
If you want to use both a membership provider w/ SQL Database and a social provider, ACS would probably be a good option.