Testing for Mensa
General Information
The only eligibility requirement is scoring in the top two percent on an approved intelligence test that has been properly administered. Mensa has its own test, which is given on specific dates by local groups. It is also allowed to submit officially-written scores (supplied by the agency that provided the test) on an approved test, chosen from a long list. Because most IQ tests are not valid for children under the age of 16 (though Mensa has members as young as 4 years old), a local office should be contacted. There are no online tests that are valid for membership (all tests must be proctored), but the "Mensa Workout" is available online and may be taken as a pretest to help individuals figure out if they should apply to the group.
American Mensa's Testing Information
Tests of achievement are not accepted, only tests of aptitude or ability. No matter how long ago the test was taken, its scores are still valid. In addition to Mensa-provided exams, more than 200 other scores are permissible, including those from the California Test of Mental Maturity, Stanford-Binet Form L-M, long form Wechsler scales, the Miller Analogies Test, and the LSAT, GMAT, MCAT, and GRE tests.
About College Entrance Exams
In the past, American Mensa accepted scores from the SAT and ACT. Because the focus of both tests shifted away from something akin to IQ testing, scores after certain dates became invalid. PSAT scores after May 1993 are not accepted, nor are SAT scores after January 31st, 1994. ACT scores from after September 1989 are also invalid. Because scores are valid forever, any test results from before those dates may still be submitted for membership. The GCT tests from the Army and the Navy were also valid until those tests changed, so only scores from before October 1980 are acceptable.
Source (for Nanosecond's writeup and portions of mine): http://www.mensa.org/info.html
Additional sources: http://www.us.mensa.org/join_mensa/priorevidenceFAQ.php and http://www.us.mensa.org/join_mensa/testscores.php3