If you are looking to get a quick game of Mahjong in, there are a number of clients and websites that you can go to.

Tenhou (tenhou.net)

Tenhou is the go-to site for a quick game. No need to register, insane stat and game tracking if you do, the ability to watch endless replays or almost-live high-level games, and an easy interface make Tenhou the best place that we know of. For english instructions, go to Arcturus’ Tenhou Documentation.

Topaiou (www.topai-ou.com)

Topaiou has, overall, a more capable player base, but not as easy-to-understand UI and setup as Tenhou. Still, something to check out if you are getting upset with ragequitters on Tenhou.

Pairon (www.pairon.jp)

Kind of a level-up-your-avatar cute girl mahjong client. Get used to playing closed tanyao, and for the huge client download.

Gamedesign (www.gamedesign.jp)

A Flash site with an excellent one-player Mahjong Flash game. Great to practice on while you are first learning.

Billy Vs. SNAKEMAN (www.animecubed.com/billy/)

The online game run by the creator of this blog, BvS has a really good one-player Mahjong area, with hidden prizes and items and stuffs, not to mention playing against some pretty excellent parody characters. Not to be missed. :)