I am looking for online games or puzzles which have a mathematical flavor and are suitable for general audiences. A classical example is the online version of Set Card Game. Or this game that has some aspects of graphs.
I'm very interested in these as well as physics games. I think they are accessible ways to get students or citizens involved in doing mathematics as mathematicians do it. The following are some of what I have found and collected online with eye towards encouraging reasoning. Stack Exchange wouldn't let me post too many links here, so I collected them in a Tumblr post: http://mathhombre.tumblr.com/post/45269554617/online-games-with-some-math-content
Traditional: Minesweeper and Lights Out.
New, in rough order of how much I like them.
I'll also mention Robert Abbott's lovely logic mazes, http://www.logicmazes.com/