Today in the West, the swastika is identified almost exclusively with Nazi anti-Semitism. This makes it difficult for other groups to use the symbol to represent more benevolent concepts, which the symbol has frequently embodied for thousands of years.
HinduismThe swastika remains a major symbol of Hinduism, representing eternity, particularly the eternal and ever-present force of the Brahman. It is also a symbol of the present of goodness, as well as representing strength and protection. The message of eternity in the swastika is also widely used by Buddhists.
Some of the oldest examples of swastikas in the world can be found in India. The Nazis saw themselves as the purest example of the ancient Aryan race, which corresponded to speakers of Indo-European languages. Because those languages are understood to come originally from India, the culture of India held some importance to the Nazis (even though present day Indians did not, since they have too dark of skin and other "inferior" traits.)
The symbol commonly shows up in religious texts, as well as the thresholds of buildings.
JainismThe swastika is a symbol of rebirth and the four types of beings that one can be born into: heavenly, human, animal or hellish. Three dots are displayed over the swastika, which represents right knowledge, right faith, and right conduct. It is these concepts that help a soul eventually escape the cycle of reincarnation altogether, which is the goal of Jainism.
Not only does the swastika show up in holy books and doorways, like that of the Hindus, but it is commonly used within ritual as well.
Native AmericansThe swastika shows up in the artwork of multiple Native American tribes, and it has a variety of meanings between tribes.
Europe Swastikas are more rare in Europe, but they are widespread throughout the continent. Often they appear entirely decorative, while in other uses they probably had meaning, although the meaning is not always clear to us now.
In some uses, it appears to be a sun wheel and relating to the sun cross. Other uses have association with thunder and storms. Some Christians used it as a form of the cross, the central symbol of salvation through Jesus Christ. It can even be found in some Jewish sources, long before the symbol took on any anti-Semitic meaning.
Left-facing and Right-facing SwastikasThere are two forms of swastikas, which are mirror-images of each other. They are commonly defined by the direction the upward arm is facing: left or right. A left-facing swastika is made of overlapping Z's, while a right-facing swastika is made of overlapping S's. Most Nazi swastikas are right-facing.
In some cultures, the facing changes the meaning, while in others it is irrelevant. In attempting to deal with the negativity now associated with the Nazi version of the swastika, some people have attempted to emphasize the difference between the facings of different swastikas. However, such attempts produce, at best, generalizations. It also presumes that all swastika uses come from the same original source of meaning.
Sometimes the terms "clockwise" and "counter-clockwise" are used instead of "left-facing" and "right-facing." However, these terms are more confusing as it is not immediately obvious which way a swastika is supposedly spinning.