Warning, spoilers are listed throughout this page.
There were five original Clans: ThunderClan, ShadowClan, RiverClan, WindClan, and SkyClan. However, it is revealed that SkyClan was driven out of their territory after it had been destroyed. Firestar goes on a journey to find them, and successfully finds the lost Clan. He and Sandstorm help them learn about Clan life. In the fifth series, A Vision of Shadows, Twigbranch brings SkyClan to the lake territories. As of Darkest Night, the fourth book in the fifth series, SkyClan has fully established itself.
Later, in Graystripe's Vow, WarriorClan was discovered. In the sixth book of the Prophecies Begin, BloodClan entered the forest, too. Below, in Categories, you can find WarriorClan, BloodClan, and StarClan.