A personality test usually takes the form of a set of questions you answer about yourself and then the test results tell you what you just told it. Most personality tests require a frightening level of honesty with yourself.
You can find a number of personality tests on the web, but most of them have the scientific basis of phlogiston -- they look good on paper, but utterly meaningless.
Personality science/personality psychology was the creation of Carl Jung. Carl Jung, who was a bit of an occultist, tried to ascribe a set of types to people, not unlike astrological signs, depending on which internal instincts and drives we prefer to use in order to function, that is, "functional types". At the same time, another psychologist, Kretschmer, claimed that there were different types, but used utterly different language from Jung. At the time, though, there was a focus on everything coming from a singular drive, the most famous being Freud's idea of Eros. Isabel Myers took Jung's work and extended into a test that could be used to separate people into types. The system was based on four independent axes where someone was usually one side or the other: Extraversion vs. Introversion, iNtuition vs. Sensing, Thinking vs. Feeling, Judging vs. Perception. One letter from each of these forms one's Myers Briggs Type; the last time I took the test, I came up with ENFP (which is odd for a software engineer).
David Keirsey then used their work as a foundation for his own, which as well as his own developments involved several successful books about a tendency he termed the Pygmalion project, that is to want people to have our personality. Keirsey disagreed with Myers' idea of introversion vs. extraversion. Keirsey then took Keirsey felt that iNtuitives were too likely to be ascribed as being introverts. He also felt that there were four major classes, based on the Myers-Briggs type letters, that were the dominant portion of a person's personality: The Guardian with an emphasis on Sensing and Judgement (SJ), the Artisan with an emphasis on Sensing and Perception (SP), the Idealist with an emphasis on iNtuition and Feeling (NF), and the Rational with an emphasis on iNtuition and Thinking (NT). It is obvious from this that Keirsey considered the Sensing vs. iNtuition dynamic of the Myers-Briggs Type to be the core division.
Then a researcher at Berkeley proposed produced the Big Five theory, which is the current focus of much personality science. Instead of classifying people as one thing or the other (a bimodal distribution), they assumed a normal distribution where relative values are important. They decided that five statistics covered the range, rather than four, largely adding an emotional stability dimension to the Myers-Briggs types (there are many, many different names for these statistics; the one I recall was OCEAN, for Openness Conscientousness Extraversion Agreeableness Neuroticism). This attempts to indicate that relative levels make as much of a difference as whether or not someone's on one side of an arbitrary mark. Proponents of this test like to poke at the Myers-Briggs work as being similar to astrology.
One exception to the statement I introduced at the beginning was the Maykorner style of test. In a Maykorner test, one is often asked for favorite colors, actions in a given unusual situation/dream, and other random bits which are them claimed to correlate with given traits. Alternatively, you might have to draw a picture. I cannot speak for the science behind these tests because I have not read much about it anywhere.
Major Personality Tests and Where To Take Them Online
If you're looking for all sorts of tests, with a wide validity range, check out Barbarian's Online Test Page at http://www.wizardrealm.com/tests/
. For lots of personality science information, check out the comprehensive, though dry, Personality Project at http://pmc.psych.nwu.edu/personality.html