New Age, if we discount some people afraid of it, refers to a religious movement whose roots lie in spiritism and the Theosophical Society, through which it is linked to the Western Esoteric Tradition (and so back to Gnosticism). Unlike many religious groups, New Age practitioners engage in an eclectic set of practices, often as a adjunct to another religion (often Christianity, which will be touched on again below). Overall, the New Age is about assembling one's own path, though often with the aid of an already-ascended guru, but there are common threads in the movement that can be used to distinguish between it and other movements.
Separation of spiritual and material planes
New Agers often believe that there is a higher plane of existence. This plane, the spiritual, is often seen as good, while the material plane is considered "lesser" or even bad. Those who know what the Gnostics thought will find this familiar. Oftentimes they are occupied with awakening their "higher self" or "higher consciousness". Some groups dislike the material to the extent that sexual activity is discouraged, often as being an obstacle to enlightenment. Sometimes the higher levels occur in a set of onion-like layers, as if to suggest concentric spheres. This separation between the sacred and the profane along physical lines was one of the few things drawn into mainline Christianity from Gnostic thinking, and is perhaps the reason why some New Age groups consider the material world and its pleasures in a sense that bears an odd resemblance to Fundamentalist Christian views.
Belief in a shift of worldview
New Agers believe that this ascension to the higher self will eventually reach a point where enough people have been transformed that a shift in overall consensus reality occurs. This shift may be accompanied by world changes, particularly cataclysmic ones, producing a New World Order aka the Age of Aquarius. In this new order, everyone will be happy, and the problems of human existence (disease, war, etc.) will disappear. The degree to which this is a paradise ranges from sub-utopian to a fairly literal Heaven on Earth.
Belief in a single, unified, divine force
In the New Age, there are rarely the compartmentalized deities that one finds in Neopaganism or even to a lesser degree in Christianity. While individuals may
lean towards monism, pantheism, or panentheism, the overall tone is that divinity is a single force. Deities, when they do appear, are decidedly examined from the perspective of being Jungian archetypes. Because of this view of a single divine force, it is felt that all religions are valid, though some make it easier than others to ascend to illumination. In some viewpoints this means that eventually all religions will eventually combine into a single, universal religion. This unified force is often mixed with a concept of energy (for which the physics definition of "ability to do work" can be interpreted in a new way).
Because of this view of a unified, divine force along with the separation between material and spiritual, there is a tendency to view the spiritual as being purely good, full of sweetness and light. This extends to a thread of optimism running throughout the New Age viewpoint and is perhaps the biggest reason for the dislike of the New Age — the Pollyanna view can become grating, especially when accompanied by gullibility caused by a belief that spiritual things are always true.
Reincarnation and Karma
In pages lifted from Hinduism (and scribbled on, of course), after death New Agers believe that they are reborn into another human body, often with a life determined by the deeds done in life. Like everything else, an individual's concept of reincarnation can be highly variable, ranging from transmigration-oriented beliefs to an unending cycle of lives without reason. Similarly, karma can be considered in ways ranging from the simplistic to the thoughtful.
Things New Agers Are Associated With
Having pondered all of this while writing this node, I would like to say that there is a resemblance between the New Age and a sort of scrubbed Thelemic philosophy.
Resources:
This came in large part off the top of my head, but some guidance was obtained from the
Ontario Consultants on Religious Tolerance at
http://www.religioustolerance.org/newage.htm.