I've been playing a lot of mahjong lately, mostly of the electronic variety since it is kind of hard to get a group of Americans together to play mahjong. Luckily for me, there are many great electronic versions. MAME(the multi machine arcade emulator) should be any electronic mahjong enthusiast's first software acquisition. Once you've installed MAME, the excellent Mahjong in MAME site has everything else you need, other than roms, to get started: rules, controls, mahjong game reviews, etc. The site is more or less essential if you don't speak Japanese since most of the mahjong arcade games originate from Japan. There are also some interesting differences between japanese rules and the traditional chinese game.
There are also many versions of mahjong for game consoles, provided you can play japanese imports on whatever system you may have. I have Minna no Mahjong for the DS(which is region free), but I wouldn't recommend it to the non-Japanese capable. One nice thing about the console versions is that they often allow you to play standard 4-person mahjong while most arcade games are 1-on-1 versus affairs.
The only other mahjong game I have played outside of emulation is Devilish Mahjong Tower( 麻雀 惡魔 塔) for the megadrive. Devilish Mahjong Tower is a product of the Taiwanese company C&E, Inc. and is a 1-on-1 versus style mahjong game where you face off against all manner of aliens in a cyberpunk future! To the death! As you can see, I am somewhat enamoured of this game. The best thing about it is that it is in Chinese, a surprisingly hard thing to find considering that mahjong is a traditional chinese game. And, as you can see, the game is also the source of my Blogger avatar.