Very few magic-centered religions have survived from a time when this was probably the primary way of belief. Both in the East and the West, conversions to the other types of religion (exemplified by Buddhism in China and Christianity in Europe) led to its gradual extinction in these areas. Even in regions where unbroken indigenous traditions exist, the populations have often been greatly diminished, and the practices encroached upon by modern society.
However, during the last century, interest in magic and in religions which speak to the issue of magic has experienced a dramatic resurgence. This phenomenon has been given a number of names, including "New Age," the "Age of Aquarius," and from a less charitible perspective, the prelude to the apocalypse. Some have also argued that it is a reactionist movement in response to what has been termed the "New Great Awakening," though to the extent that it is occurring outside the confines of the United States, this premise is questionable.
The following list of religions we believe to be "Magic Centered" is hopelessly incomplete, as new candidates are probably appearing on a daily basis. However, if there is something you know we've forgotten, don't hesitate to let us know.
In addition to true religions, we can enumerate some "philosophies" that fall into the same basic group. For example, The Teachings of don Juan by Carlos Castaneda, and Illusions by Richard Bach both have amassed collections of "believers," even though (to our knowledge) there is no church or organization that espouses these beliefs. This is partly a result of the fact that many of these belief systems promote (or are at least harmonious with) solitary practice, as Scott Cunningham recognizes in Wicca for the Solitary Pratitioner.
What you'll generally find in common about these religions is a belief that magic is a personal, experiential phenomenon, and one that can be either positive or negative depending on the desires of the individual. Many recurring themes are found, such as the belief that help you give or harm you inflict will come back to you, often amplified (e.g. the threefold law of Wicca).