Started in New Jersey in 1942 by L. Ron Hubbard as a successor to his earlier self-help system, Dianetics. Scientology teaches that people are immortal spiritual beings who have forgotten their true nature. Thru their practices a Scientologist may progress toward the Clear state, winning gradual freedom from the reactive mind's engrams, and acquiring certainty of his or her reality.

It has gained notoriety recently because of publicity generated by celebrity members. Some are jazz pianist Dave Brubeck, actors and actresses Tom Cruise, John Travolta, Kirstie Alley and Elisabeth Moss, Singers Sonny Bono, Isaac Hayes, TV host Greta Van Susteren.
Former members, Lisa Marie Presley, football player John Brodie.
See List of Scientologists at Wikipedia

Hubbard envisaged that celebrities would have a key role to play in the dissemination of Scientology, and in 1955 launched Project Celebrity, creating a list of 63 famous people that he asked his followers to target for conversion to Scientology.

See: Closer Online

Scientology teaches that people are immortal beings who have forgotten their true nature. Its method of spiritual rehabilitation is a type of counselling known as auditing, in which practitioners aim to consciously re-experience painful or traumatic events in their past in order to free themselves of their limiting effects defined as engrams left behind.
During the auditing process, the auditor may collect personal information from the person being audited.

Number of members:
Scientology has claimed millions of members forever, but this counts anyone since L. Ron Hubbard first came up with Dianetics in 1950, who have ever picked up a Hubbard book, or filled out a "personality test," or taken a course, or otherwise had any interaction with the organization in any way.

In 2008 Trinity College in Hartford, which has been surveying Americans about their religious affiliations for more than 20 years released new data in it's American Religious Identification Survey (ARIS)
In 1990, ARIS had found about 45,000 Scientologists. In 2001, it found 55,000, and in 2008, it found 25,000.
Adherents.com says there are 500,000 worldwide.

The Scientology symbol closely resembles the Christian cross, but differs from it with the addition of four diagonal rays between the conventional horizontal and vertical arms. The eight points of the cross represent the eight dynamics in Scientology:

1. The Self
2. Creativity, sex, and procreation (family)
3. Group, society, community
4. Species survival (humankind)
5. Life forms in general
6. Matter, Energy, Space & Time (physical universe)
7. Spirit (self or others as a spiritual being)
8. Infinity or Supreme being

Scientology and wikipedia have been having a battle over what wikipedia says is "pushing its own agenda on the site", so they have been banned. See SciTechBlog and

Links
What Do Scientologists Believe? - Beliefnet.com
wikipedia
How Experts View Scientology
Scientology cross - Wikipedia