Hindu: In Hindu, the Swastika is the second most prominent symbol, ranking second only to Omkar. The two standard forms of swastika are the right hand path (clockwise) and the lefthand path. These symbols also represent male and female in Hindu India. It has also been speculated that the swastika design was used to design a strategically superior fort. This comes from "Su Vastu" which means "good habitation".
Jain: The swastika in Jainism states that during the cycles of death and rebirth we may be reborn into the animal/plant world, hell, earth, and the spirit realm. The swastika reminds us that we should become "the pillars of the four fold Jain Sangh", to recieve liberation. This eventually means that we overcome social attatchments, renounce worldly life, and follow the path of a sadhu or sadhvi to be achieve our ultimate existence.
Taoism: In Taoist worship the Swastika is part of the Falfun Dafa, and is used as a counterpart to the Yin Yang (the Taiji). In the Falfun Dafa the swastikas rotate clockwise, symbolizing the absorbtion of energy from the universe (Ganesha - The Sun), and counterclockwise rotation symbolizes the giving off of energy (Kali-Maya - The Moon).
Buddhism: In Buddhism the swastika is a symbol of resignation.