There are many different non-violent online multiplayer games and I am going to list some for you. Some non-violent online multiplayer games are Feralheart, The World, and many more.
MAG
The most popular online multiplayer game in North America is currently League of Legends. Other popular online multiplayer games include World of Warcraft and Guild Wars 2.
Some good midieval games are... Fate (19.95) Fate Undiscovered Realms (19.95) Runescape (free online multiplayer) World of Warcraft (free 14 day trial also an online multiplayer) Wizards 101 (free online multiplayer)
wizard 101 kids and adults can play this 3D multiplayer game
just chek out nitrome.com,especially double edged.
Tetris, 2048, Bejeweled and others are all games you can find on the web. If you mean "online multiplayer", I recommend Portal 2.
xgen studios stick arena ballistic
Ha ha should have gone to windows.
The PS3 does have some 2 player games that are great without requiring online multiplayer, but most games are single player and require an online connection for the multiplayer.
If you like Pokemon Pokemon indigo,wizard101,andfor some non online fun go to addicting games
ShellShock Live. You are tanks instead of worms and it is an online, multiplayer flash game.
Some of the most popular games with dragons include World of Warcraft, and Guild Wars 2, which are both massively multiplayer online role-playing games.