The religion of the Seven Gods is Catholicism... everyone has converted to it, the dominant technological civilization with swords and medieval armor and what not all believe. The septs are cathedrals, the septons are priest, etc.
Previous to that the Old Gods worshipped by some in the North, and this might map to the Roman/Greek religions in that its been supplanted by the Seven. However, given the nature of this religion, it's more Druid-like or even Native American. Definitely has a shamanistic bent.
The religion of the Drowned God is more Norse, with the Drowned God being some hodge-podge of Odin and Loki and the Iron Islanders something like Vikings.
The Many-Faced God and the Braavosi religion is something like the mystery cults from around the time of the birth of Christianity. Disciples struggle for years to qualify for new knowledge, and the masses never do.
Melisandre and her fire cult... not really sure. The dualism of it it sort of like Zoroastrianism, at least in a shallow way. But the way it's portrayed on the show seems more like a modern cult. The way she keeps very stern control of her disciples, all true believers that are certain that they (and their religion) will change the world for the better and in the short-term... that doesn't fit so much.
And I can't even begin to speculate on the religions of the cities in Essos. There are hints of the Babylonian and Egyptian pantheons, at least that's the impression I get, but nothing I can point out with a finger.