Just when I was sure that I wouldn't find a free turn based strategy game for linux, out comes the UFO: Alien Invasion tech demo. Inspired by the "X-COM" series of games, UFO:AI puts you in charge of a squad of 8 with different strengths and weaknesses, bound together by the common goal of eradicating the alien infestation and using their own technology against them. OK, there's basically no plot, but keep in mind: this is only a tech demo.
Don't let the phrase "only a tech demo" above fool you into thinking that there is no gameplay to be had. The demo comes with three missions, full of alien-killing, civilian-saving fun. It's built on a modified version of the Quake2 engine, so although the graphics are nothing to wet your pants about, they're not ugly at all. As far as I can tell from the limited amount I've been able to play, this seems like a game that could shape up to be very interesting.