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I don't know how many are familiar with the Fire Emblem series, but for those who are it's a single player turn based strategy game made by Intelligent Systems.
Info on FE found here: http://en.wikipedia.org/wiki/Fire_Emblem
Now the link above is a link to a forum/game that make Fire Emblem into a balanced and fun multilayer game. Your characters are completely customizable, even down to uploading custom sprites to use in game. There is also no download, as long as you don't use IE, the game runs entirely in your browser.
It's a lot more laid back than LoL since you can just log in, take your turns on your matches and go on with the rest of your day, instead of setting aside and hour+ for one game. The community is ALOT nicer and more helpful than 90% LoL players.
If you're interested in TBS games or just want a calmer community, please check out the site. There are some issues with validation, but after that, you're golden.