Overview of Beliefs

Animism: the belief that all things have their own inherent spirit and self-awareness. Rivers, rocks, thunderstorms, trees, etc. Even man-made things can be imbued with a spirit inherited from its users and its surroundings. Animism is often believed to be the first belief system, and later developed into polytheism.

Discordianism: a religion, or anti-religion, which focuses on the Greek Goddess of Disorder, Eris – known as Discord to the Romans. Although it sees Disorder as the underlying root of all things, it truly promotes a Balanced Path within the context of Perception Based Reality.
Read the Principia Discordia

Druidism: the Druids were the intelligentsia of the Celts. While much is lost of their beliefs, neo-Druid organizations seek to reclaim the traditions as best they can. They differ from Wiccans in that they are mostly strictly polytheistic, follow the gods of the Celts (or all Indo-European pantheons – though not in the syncretistic way Wiccans often do), and they have a different ethical code.
Neo-Druid organizations:
Ár nDraíocht Féin: A Druid Fellowship
The Order of Bards, Ovates and Druids

Existentialism: a philosophy which focuses on the experience of existance, which defines life and it's meaning through our struggles to discover our selves, and to be true to our selves, while also trying to better our selves. Existential angst is the dread which comes with freedom and the necessity of making a choice, knowing it may very well be the wrong choice, but doing it anyway. With freedom comes responsibility, and with responsibility comes the ever present potential for doubt, guilt and suffering. The existentialist knows this, but takes the suffering of freedom and experience over the bliss of ignorance and pretense.

Gnosis: "intuitive knowledge of spiritual truths; an esoteric form of knowledge." When I speak of my own moments of gnosis I refer to this intuitive knowledge/understanding of spiritual and esoteric truths - and not specifically of the various Gnostic sects, even though they sought such truths as well.

Gothic/Dark Paganism: a branch of Paganism which focuses on the darker aspects of the light/dark polarity. Calls for balance, but often pays particular interest to the symbols of death and dying, honoring of the gods of death and the Underworld, and embracing the shadow self.
These articles by John J. Coughlin explain the whole concept:
An Exploration of Dark Paganism

Hard Polytheism: Hard polytheism is the belief that all of the gods are unique and individual entities, and not just different aspects of one God/dess.

Magic(k): the act of effecting change in the Universe by focusing your will on an aspect and tweaking it. There are many different kinds of magical practices and tools. High magic deals with affecting the higher realms and levels of consciousness, Low magic with the lower realms. Most people often find a balance of the two. Within each of these distinctions lie many different practices. I favor candle magic, color magic, cord magic (to a lesser extent), and trances and journey work – with the aid of music and crystals.
This site offers a decent overview of High and Low types and practices: Liber-Umbra.com

Neo-Pagan: an umbrella term for a group of diverse spiritualities which have a few common elements, including reverence/worship of the spirit(s) of Nature in its many forms. Often polytheistic, sometimes pantheistic, and less commonly animistic. Often used to refer to the revival of Western European Pagan religions.
See a more complete definition at Wikipedia

Neo-Platonism: an ancient school of philosophy which is sometimes used as the philosophical foundation for Paganism. It began with Plotinus who taught that an indescribable and transcendant One, which is beyond Being, emanated the universe as a series of lesser beings. Some see the progression of these emanations captured within some ancient creation myths.
See a more complete definition at Wikipedia
And a detailed analysis at The Internet Encyclopedia of Philosophy

Pantheism: the belief that Deity is immanent in Nature. Many people take this belief to a sort of extreme and espouse the belief that “all gods are one God”. I, personally, disagree with this statement vehemently, and will discuss it further in one of my rants.

Panentheism: the belief that ‘God’ is both transcendent and immanent. Another way of saying it is that Deity is the spiritual essence of everything within the Universe, but it’s own Essence and Awareness lies beyond the Universe as well.

Polytheism: the belief in a pantheon of many gods. See also Hard Polytheism and Soft Polytheism.

Shamanism: while most people think of the Native Americans when they hear the word ‘shaman’, there are actually many cultures which practiced shamanistic techniques and beliefs: such as ecstatic trances, vision quests, spirit guides, totems, ancestor worship, etc. My own practices are much less formalized than the Druids or Wiccans, let alone any ceremonial work. Mine are much more intuitive, and I work with guides, totems, ancestors and while I have yet to achieve an ecstatic trance, I have gone on vision quests and meditative journeys.
An Overview of Core Shamanism
Anyone truly interested in Core Shamanism should read‘The Way of the Shaman’ by Michael Harner.

Soft Polytheism: There are a few different form of soft polytheism. The first is the belief that all of the gods and goddesses are all aspects of an overall God, and is sometimes considered akin to a form of monotheism. The second is the belief that all the gods are aspects of the God, and all godesses of the Goddess. This varient is often seen as being a form of duotheism. The third is the form that I adhere to in which all of the gods and goddesses are emanations of a Universal Essence, with archetypal relationships (a sort of Universal Pantheon) - but that they also have cultural uniqueness and individuality. I try to ellaborate more fully on this concept in the essay 'The Nature of the Gods'

Taoism: The Path, or the Way. All Being is born of Non-Being and all things have a Natural way of Being… or their own Path.
For more information:
An Overview of Taoism from ReligiousTolerance.org
One of Several Translations

Theosophy: any of various philosophies professing to achieve a knowledge of God by spiritual ecstasy, direct intuition, or special individual relations. Also, A belief based on mystical insight into the nature of God and the soul. Not necessarily a part of the 'Theosophic Society' which has set beliefs and doctrine.
The Theosophic Misfits

Wheel of the Year: the modern pagan calendar as used by many neo-Pagans. It focuses on the changing of the seasons, and the interpretation of such change depending on the tradition. The Four Celtic Fire Festivals factor more heavily in my own beliefs and practices because I have Celtic leanings. However, that is not to say that the Solar Festivals don’t play their part.
An Overview of the Festivals

Wicca: a belief system first established (or popularized) by Gerald Gardner around the 1950s. It is a syncretistic belief system which focuses on the Triple Goddess and the Horned God. It is influenced by pre-Christian Celtic beliefs, as well as ceremonial organizations such as the O.T.O. The main ‘moral tenet’ of Wicca is the ‘Wiccan Rede’ which states “an it harm none, do as you wilt” – or some variant therein. They also believe in the Threefold Law.
A Comprehensive Overview Focusing on the Starkindler Tradition

Withcraft: a particular type of magic which deals predominantly with the realm of low magic. You hear the term a lot, and practicioners who call themselves witches often deal with candle magic, minor divination, herbology and crystal magic. I prefer low magic, as I work intuitively and ‘as the spirit moves me’, rather than in with organized formula and ritual. However, I do not consider myself a witch as I am primarily interested in the spiritual aspects of my beliefs as opposed to the magical.

Wyrd: a concept of Fate found in some Norse and Anglo-Saxon traditions which emphasizes that Fate is fluid, not static, and is constantly being woven based on the choices we make, our Orlog, and our Predispositions.
My idea of Wyrd came from reading 'The Way of Wyrd' by Brian Bates

**I gleaned many of these definitions from Religious Tolerance and Wikipedia