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Godville is exactly that.
You're a God to a single Follower and every so often your follower will pray to you giving you power. You can use the power to heal or harm your follower. Mines 3 years and 9months old.
Your follower will fight creatures, trade for new gear, get drunk at the tavern, build a temple for you, and even learn special abilities. You can get a pet, join a guild and add friends which will interact every once in a while.
I have like 15 friend invites if anyone wants one.