OK, since I read up a bit on the Traditional Mahjong history in western culture, variants, etc. Here is what I found out.
Interesting enough, it looks like Mahjong in the West began with Abercrombie and Fitch in 1920. I guess old man Fitch was importing goods from Asia and figured it would be a good idea to bring this game over to America. The game hit it big in New York, and all the yuppies felt more sophisticated and cultured for playing the game, and it was at the height of fashion.
Along comes this businessman by the name of Joe Babcock. He decided it would be a good idea to make this game hit the mainstream of America. In classical American fashion, he dumbs down the rules of the game for the sake of "acceptability". The game hits it pretty big in the US, but since Babcock butchered the rules, the game is only a short lived fad.
Now the game is gone and not forgotten by the late 30's. It is adopted again by a group that formed called the National Mah Jongg League (NMJL), as well the US Military. In WWII, it becomes a popular game for the GI's to play. The Military stuck mostly with Babcock's rules, but fixed the major problems with it. The NMJL creates their own set of variants as well, and they are the ones, as Spacejack mentioned, who change things around on an annual basis as well. Apparently, this is the largest Mahjong playing group in the West, so if you want to play in a Mahjong club, chances are the NMJL annual rules are the rules you adhere to.
I found this tree picture thing that someone posted showing the family tree of Mahjong.

KEY
(Clockwise from trunk at 6:00, then from treeline down to roots)
CHINESE CLASSICAL - the game that took the world by storm in the 1920s
JAPANESE CLASSICAL - the Japanese take on the classic game
RIICHI/DORA - the way it's played in Japan today
KOREAN - the way mah-jongg is played in Korea
WMPA - World Mahjong Players Association (http://www.wmpa.net), Korea
TAIWANESE - the 16-tile game played in Taiwan
FILIPINO - the 16-tile game played in the Philippines (everything is coming up flowers!)
CANTONESE (HKOS) - the simpler take on the classic game
NEW STYLE - uses the modern Japanese take on many hands
12-TILE - like HKOS, only one tile exists only in the player's mind
OFFICIAL - the rules permitted in China today
ZUNG JUNG - Alan Kwan's simpler-scoring version
MMM - Mahjong Masters Millions rules (created for a tournament that never was)
HUNANESE - uses only the 108 suit tiles
SINGAPOREAN - uses special flower tiles that can capture each other
INDONESIAN - uses a DORA-like wild tile
VIETNAMESE CLASSICAL - uses a set of 160 tiles (jokers and extra flowers)
VIETNAMESE MODERN - uses a set of 176 tiles (lots more jokers)
BABCOCK - the game as Babcock introduced to America in 1920
WHITNEY - the "American" rules described by Whitney are not precisely Babcock, not precisely Western
WESTERN - the rules used in Australia and the Asian subcontinent today
WRIGHT-PAT - Wright-Patterson rules (used on American military bases)
NMJL - National Mah Jongg League (yearly card of hands; no chows)
MHING - card game very similar to Western
CANASTA & GIN RUMMY - The popularity of these two card games nearly killed mah-jongg in the 1930s
TILE-MATCHING SOFTWARE - the plethora of computer games incorrectly calling themselves "mah jongg" have got the world confused as to what mah-jongg really is (1986 to present)
PROTO-MAHJONG (ground level - the line of grass separating roots from trunk) - the unknown original Chen Yumen rules
YEH-TZU - ancient Chinese dice game (9th century)
MATIAO - ancient Chinese trick-taking card game (40-card deck) whose four suits led to the mah-jongg suits (Ming era, 1368 - 1644)
KHANHOO - card game described by Culin (1924), played with Kun P’ai cards described by Wilkinson (1895), which led to the gameplay of mah-jongg
DOMINOES - the form of these ancient game devices inspired the tile form of mah-jongg. Egypt's King Tutankhamen had a set of dominoes as far back as 1355 BC. They were entombed with him and today are on display in King Tutankhamen's Museum, in Cairo.
The tree is from
http://www.sloperama.com/mjfaq.html