While it's unlikely to play a major role, you've undoubtedly heard Tyrion Lannister mention the gods of Old Valyria, a civilization which was destroyed in the Doom of Valyria. This polytheistic religion greatly motivated Daenerys's ancestors, inspiring fearsome dragon names. It's not vital to know this information since nobody in the show follows these gods, but it's definitely interesting background information!
Where the religion is (was) based: Old Valyria
What followers believe(d): Followers believed in multiple gods, a few of whom inspired the names of several Targaryen dragons. (Think: Balerion, Vhagar, Meraxes, and Syrax)
Who follows this religion: now-extinct Valyrians, including the Targaryens
