While mahjong is traditionally played with tiles and people, the game can be played with videogames against AI (computer) or online, or both. Playing any computerized version of Japanese mahjong, a player does not need to worry about game setup, tiles, scoring, and the lack of players. Aside from the lack of players problem, everything else involving the game is done automatically. Thus, a player may simply worry about developing hands and effectively playing the game.
Online play sites:
Flash game
http://www.gamedesign.jp/flash/mahjong/mahjong_e.html
You can practice these basic rules against three computer players at the following site. Everything is automatically taken care of for you except that you need to have a yaku in order to win a hand.
Shin Jan Ryu Mon
http://www.ncsoft.jp/janryumon
There is a tutorial for non-japanese-speaking players, which can be found here.
Tenhou
Tenhou game session
Games at Tenhou are available for free. Anyone who wishes to have their stats tracked for ranking purposes, may register for free, although some advances features are restricted to paid subscriptions. English instructions to navigating the site can be found here.
Regardless of the time of day, enough players can be found in Tenhou.
Ron2
Players at this site may sign up for a 6-month trial period, and then they may choose to continue with a subscription. Yet, declining the subscription, players are still allowed to play one game a day. With a subscription, players may have the privilege of playing against some Japanese professional players.
Maru Jan
Maru Jan is a relatively new system, with its upgraded graphics. Scoring here is modified such that a 4 han and 30 fu, and 3 han 60 fu is equated to that of a mangan. This means the optional rule known as "Kiriage Mangan" is active.
Pairon
After an extensive Japanese heavy user signup process, you have the privilege to play mahjong here with some moe and/or loli avatars.
Sega Mahjong
Sega has it's own programs to play mahjong derived from their arcade games. You can download a PC version, Android, and iPhone versions. You need to download the client and start the program which will ask you to create an account. In the free mode you can play Tonpuusen, East Round only. Or 3 player game. Also you can play mahjong against CPU (same game modes as free), and you can create you own room. Other types of games need payment.
Janrevo
Another japanese mahjong site. You can play free. The premium players have various benefits, as Treasure Points to earn, score sheets review, more detailed info on your plays, long time thinking (limited to a few usages per game), being able to reach Dan levels, can use a player CPU if you're away from keyboard, and when a hand ends you can open the hands of the other players if you're interested.
Apps
Available for Android and Apple devices, the game Jan Ryu Mon is available. Also Mahjong Fight Club and Mahjong Tengokuhai are good options to play online (both games have no english). Other apps, like Nagomi or Pro Mahjong Kiwame, are also available, but these are limited against AI (computer) opponents.
Some games as Mahjong Tengokuhai have online and offline modes.
A Saki app. is available for free in the Android market which gives the player a selection of characters from the series to use as an avatar in matches. The app also keeps track of stats such as win percentage and yaku used in winning hands.
Apart from those mentioned games there are other options to play, offline and/or online, japanese mahjong (or other variants). Most games are only in japanese, or other asian languages, depending on the variant and/or the manufacturer.