There seem to be six or seven different religions with even more Gods?
In the "modern day" era of the Song of Ice and Fire there are quite a few different religions, but figuring out how many "gods" there are is a bit tricky.
On Westeros (the continent where most of the non-Danaerys scenes take place) the primary religion is the Faith of the Seven; this is the official religion of the Seven Kingdoms as a whole, though not all of the seven former kingdoms follow it. The Faith of the Seven, not surprisingly, worships seven gods: Father, Mother, Warrior, Maiden, Smith, Crone and Stranger. They believe that the Seven are seven aspects of a single god, who once walked among the Andals (the ancestors of most of the people in southern Westeros). Whenever you hear about a "septon" talking, or people visiting a "sept", they are talking about the Faith.
In the North, people still largely follow the religion of the First Men (the ancestors of the Northerners), who worship the old gods. Here's where trying to count the gods starts to fall apart, because worship of the old gods is what we would call an "animistic" religion: they believe in lots and lots of nameless gods, inhabiting the elements of nature. In particular, followers of the old gods pray to specially formed weirwoods trees; the Children of the Forest believed that each tree was a god, and part of a vast collective of godhood that spanned all of nature.
On the Iron Islands, the Iron Men also still follow their ancestors' old religion; not surprisingly, theirs is based on the ocean. They follow a dual theology: they worship the Drowned God, but also believe in his enemy the Storm God. Priests of the Drowned God are baptized in water by literally being drowned and resuscitated.
A new religion that is starting to spread in Westeros is the worship of R'hllor, the Lord of Light. This is a religion that was imported from Essos (one of the other continents, across the Narrow Sea from Westeros) but has started to take hold in Westeros. Melisandre, the Red Woman travelling with Stannis Baratheon, is a priestess of R'hllor, and is spreading the religion among Stannis' army. Worshippers of R'hllor also believe there are two gods: R'hllor, the Lord of Light, and his arch enemy The Other.
Across the sea, there are dozens of small, isolated religions of varying sizes. On the television show, I believe we've seen the Many-Faced God of the Faceless Men, the Great Stallion of the Dothraki, and the worship of Mother Rhoyne along the Rhoyne River in Volantis. In the novels, there are brief mentions of at least a dozen more.
Some other gods:
The Great Shepherd or lamb god is the deity of the peaceful Lhazareen. They are taught that all men are one flock.
The Old Man of the River is a lesser god of the Rhoynar. He is the son of Mother Rhoyne and his form is that of a giant turtle. He fights the Crab King for dominion of all life below the flowing water. (In "A Dance with Dragons" when the Shy Maid sails down the Rhoyne at Ny Sar they see a huge horned turtle, which Yandry claims is the Old Man of the River).
The great goddess of the Unsullied is called by many names, including the Lady of Spears, the Bride of Battle, and the Mother of Hosts. According to Grey Worm, her true name belongs only to the ones who have burned their manhoods upon her altar. The Unsullied purify themselves according to the laws of their great goddess; one way is to bathe in the salt sea. The Unsullied may not speak of the great goddess to others.
You can find more gods in "The World of Ice and Fire".
Some of the Gods that have been missed by previous two Answers are following:
- Lady of the Waves- a goddess of the Sistermen worshipped on Isles of three sisters before Andals came with their seven gods.
- Lord of Skies - a god of the Sistermen worshipped on Isles of three sisters before Andals cast down local faiths of Sistermen.
- Aquaan the Red Bull - A god of Braavos.
- Bakkalon aka Pale Child - A god of Braavos usually associated with death and worshipped by soldiers.
- The Black Goat - A god of Qohor.
- Hooded Wayfarer - A god of Braavosi usually worshipped by the poor.
- Lion of the Night - A god of Yi-Ti worshipped by rich men.
- The Merling King - A god of Braavos worshipped by sailors.
- The Pale maiden - A goddess of Braavos worshipped by sailors.
- The Pattern - Not exactly a god, rather a religion. Practised by Lorathi people.
- Semosh and Selloso - Brother gods from Braavos.
- Silent god - Another god from Braavos.
- Stone Cow of Faros - A deity worshipped in city of Faros situated in Great Moraq island.
- Trios - As evident from name, A three headed god worshipped in Free city of Tyrosh.
- Weeping Lady of Lys - A goddess worshipped by Lyseni people and some Braavosi.
This thread doesn't account for the possibility that many of these gods are perhaps the same god just known by other Names. And perhaps the Andals with the seven or the faceless men with the many faces god have a greater understanding, maybe they are all one god with many different aspects/faces.