Eleusis technically belongs to the eights group, in that players try to get rid of their cards by playing them to a discard pile. However, the unique feature of this game is that the rule governing which cards can legally be played is initially unknown to the players. The dealer (sometimes known as God) secretly invents and writes down the rule governing play. The other players try to guess the rule by observing which plays are legal.
The original version of Eleusis was invented by Robert Abbott in 1956, and was published in Martin Gardner's column in the Scientific American in June 1959. It subsequently appeared in Gardner's 2nd Scientific American Book of Mathematical Puzzles and Diversions and in Robert Abbott's book Abbott's New Card Games (Stein & Day 1963).
In the 1970's Robbert Abbott made some major improvements to Eleusis, including the option for a player to become a prophet and try to predict whether each play would be called legal or illegal. This current version The New Eleusis was published in the Scientific American in October 1977. Robert Abbott's booklet about Eleusis can be ordered from his web site - it gives a fascinating account of the development of the game, as well as rules and advice on play.
Here is a link to David Matuszek's page, with a summary of the rules of Eleusis.
Dave Moser has set up an Eleusis registry where people wishing to play the game can leave their contact deatils, and find details of other players in their area.