The Enneagram is a nine factor personality system that is sort of a historical mutt, many different influences. The nine factors are - orderliness, helpfulness, image focus, hypersensitivity, detachment, caution, adventurousness, strength, and calmness.
These tests are based on the work of Carl Jung, David Kiersey, Isabel Myers and Katherine Briggs. They are similar in underlying theory to the Myers-Briggs Type Indicator (MBTI) and the Kiersey Temperment Sorter. They measure four bipolar factors, Introversion/Extroversion, Thinking/Feeling, Intuition/Sensing, and Judging/Percieving.
These tests show you how your answers on statements or descriptive words/phrases compare to other people who have answered in the past, a useful/interesting test to see how you compare to others on different issues.
Big Five Tests
The Big Five is the most proven personality test in the academic research community presently. It is composed of 5 factors - open-mindedness, conscientiousness, agreeableness, emotional stability, and extroversion (the factor names vary a little among authors).
Right-Left Brain Tests (Brain Laterization)
These tests measure your right and left brain functions, indicating strengths and possible weaknesses, and whether you are more dominant in one hemisphere.
Other Personality Tests
Personality Disorder Test - this test is based on the 10 DSM-IV personality disorders.
Eysenck Personality Test - based on the personality theory of pioneering theorist Hans Eysenck, 3 factors - extraversion, neuroticism, and psychoticism.
Cattell 16 Factor Test - based on the work of Raymond Cattell, another personality research pioneer.
*The multi-user tests require two or more people to respond to receive results (an option to email the test is available). The single user tests are self reporting (you can provide the answers for yourself and the person you are trying to assess compatibility with).
Multi-user Enneagram Test
Single-user Enneagram Test
Single-user Jung test
Single-user Big Five Test
Word Association Test - this test displays a series of words for you to answer positive, negative, or neutral to and then displays your responses and response times.
Ask The Oracle is a decision making tool.
Query the Universal Mind allows you to type in an interest (author, band, book, movie, etc) and then searches a database of over 20,000 users to find interests which correlate with it.
Search Minds allows you to take a personality test and see what users from a large database match most closely to your personality type.
The Famous Leader test and Classic Movie test are based on a large randomized custom personality question database and contain results which are meant to be relevant and amusing.