I know you said you weren't into shooting games, neither am I, yet I found Team Fortress 2 to be a highly enjoyable game - and it's free!
Download Steam (http://store.steampowered.com/) and search for it. As someone else said, there's also a fair few other free to play games, and games under a fiver.
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Minecraft (15 euros) http://www.minecraft.net/
Spirit Engine (free) http://thespiritengine.com/tse1.html
http://ageofempiresonline.com/
There is a premium version but they say there is 40 hours of free gameplay to be had.
Download Steam (http://store.steampowered.com/) and search for it. As someone else said, there's also a fair few other free to play games, and games under a fiver.