The most prevalent method of personality typing in the Western world is the Myers-Briggs Type Indicator, developed by Katharine Cook Briggs and Isabel Briggs Myers, who based much of their work off of the theories of Carl Jung. Or so wikipedia tells me. But in fact there are many different personality typing systems--the ones I can list off the top of my head being MBTI, Enneagram of Personality, Big Five, and Socionics. In my humble opinion, Socionics is probably the best among the bunch, both in terms of accuracy and ease of application.
Socionics and MBTI are actually pretty similar--nearly the same type designations are used, although if you pay close attention, when talking about socionics, usually the J/P designation is in lower-case, while in MBTI, all upper-case is used (i.e. INFj vs INFJ). But are Socionics and MBTI different from a typing perspective? Supposedly, yes, although I've personally found that someone who is a certain type in one system will be the same in the other. I don't believe this is the consensus, however, so feel free to check out something like Socionics.com's conversion guide.
The differences between the two systems stem a lot from the definitions of extraversion and introversion and conceptually, the systems diverge a lot as soon as you get past the initial type designation. I don't consider myself an expert in MBTI, so I won't get too much into it here. I will say, that I've found that MBTI focus a lot on the positive aspects of the different personality types, where as in Socionics, there is a prevalent discussion of character weaknesses as well. Moreover, I've found that Socionics provides a much better analysis of interrelations between the types. More on those later.
Really, this post just serves as warning that I'm usually speaking from a Socionics perspective, although generally what I say will be applicable in the MBTI world as well. I'll leave you a link to some helpful socionics tests from Socionics.com.