Riichi

>New to riichi
Read this before playing
https://en.wikipedia.org/wiki/Japanese_Mahjong
http://curms.soc.srcf.net/wiki/index.php?title=A_Beginner's_Guide_To_Riichi_Mahjong
http://osamuko.com/complete-beginners-guide-to-online-mahjong-part-1-how-to-play

Or just play this over and over again.
http://www.gamedesign.jp/flash/mahjong/mahjong_e.html

>Playing on PC
Singleplayer:
Gamedesign Flash game. See above.
4Winds. Also capable of using other mahjong rules.
Saikyo no Mahjong 3D.
Touhou Unreal Mahjong. Latest version is 4N.

Multiplayer:
Tenhou. Most regularly played. No-frills, but competitive.
http://tenhou.net/0/?L7447 (change to L0 for regular lobby)
SEGA Net Mahjong MJ. Relatively popular. Also available on smartphone.
https://sites.google.com/site/mjnetguide/home
Other titles: ron2, Maru-Jan, JRM, etc.

>Playing on Android
SEGA Net Mahjong MJ. See above.
Mahjong Tengokuhai ( 麻雀 天極牌 ). Good singleplayer mode, can also play multiplayer.
https://play.google.com/store/apps/details?id=jp.co.hangame.s_mahjong
Kindai Mahjong All-Stars ( 近代麻雀オールスターズ　闘牌伝 ). Unlock characters from Kindai Mahjong series and play them.
https://play.google.com/store/apps/details?id=jp.co.cygames.tohaiden
Mahjong and Friends Japan. Singleplayer for plebs.
https://play.google.com/store/apps/details?id=com.mjguy.android.games.mjfjpfree

>Manga
Akagi series. Mahjong for gentlemen with sharp nose. Also includes Ten, Hero, and Washizu.
Saki series. Mahjong for lesbian. Also includes Side-A: Achiga and Shinohayu.
Tetsunaki no Kirinji. Story of 7447 scrub plays IRL. Also includes Kabuki-hen.
Others: Tetsuya, Mudazumo, and other titles from Kindai Mahjong.

>Anime
Akagi, Kaiji, Saki, etc. Basically same as above.

>Live Action
Janki/Shin Janki.
Tohai.
Akagi.

>Further reading
http://www.mahjong.guide/
http://osamuko.com
http://justanotherjapanesemahjongblog.blogspot.com
http://riichi.dynaman.net
http://arcturus.su/tenhou/ and http://arcturus.su/wiki/