--- EDIT ---
The answer assumes that you're going to use HTTP for communication between your game and your backend database.
One choice would be to implement your own authentication and authorization mechanism.
Basically, you should have some sort of API on the backend system (database) and protect that via some auth mechanism:
- signed requests
- basic authentication (good for internal applications & consumers of the API)
- oauth (good for external 3rd party consumers of the API)
Second choice is to use a platform that gives you backend as a service (BaaS). Most of these providers also give you a lot of security mechanism like oAuth server for instance and you don't have to worry for the backend infrastructure a lot. You just have to worry about how you're going to use it.
Checkout apigee and Parse for the second option.