Abbreviation	English Name	Japanese Name	Link to Official Web Site
JPT	Japanese Proficiency Test	日本語能力試験	http://exam.ybmsisa.com/jpt/japan/japan01_1.asp
JLPT	Japanese Language Proficiency Test	日本語能力試験	http://www.jlpt.jp/
BJT	Business Japanese Proficiency Test	ビジネス日本語能力テスト	http://www.kanken.or.jp/bjt/english/index.html
J.TEST	Test of Practical Japanese	実用日本語検定	http://j-test.jp/

The JLPT is by far the most recognized among these, and often required by employers or schools.  There are currently five levels, with N5 being the easiest, and N1 being the most difficult.  The test if offered only once per 6 months for most levels, and you can take at most one level on any particular test day.

JPT is basically a test designed to mimic the JLPT questions and format, while giving the results as a single score (similar to TOEIC), instead of having multiple levels of tests.  There is a mapping of what ranges scores on the JPT tests corresponding to passing which levels of the JLPT.  JPT is essentially focused on Koreans and Chinese, It seems to be a good way to gauge your skill level before committing to which JLPT level to take. (Although the price is similar at around 5000 JPY).

BJT : This test is focused on vocabulary and grammar used in the work place, and used to be called JETRO.  (The test name changed because it is now administrated by a different organization).

J.TEST is supposedly a test of practical Japanese, as opposed to the academic nature of the JLPT or the business focus of BJT.