I have a full-time job and family so I enjoy the flexibility of a turn-based strategy game: spending a whole weekend playing with the kids, or taking a few turns during lunch breaks. Sid Meier's Alpha Centauri is one of the best examples of this kind of game. Playing from the viewpoint of 7 different political factions, each with their own ideas about colonizing the planet, and with different built-in advantages, means you have a different game each time. The narrative breaks get you into the plot from the word go. The interface is superb - intuitive, with an easy tutorial that means you almost never have to dip into the manual!
If you prefer a more thoughtful style of game to the shoot-em-up type, do give this a go. And once you've played it to death, you can try the Alien Crossfire upgrade which lets you also play one of two warring alien factions, or 5 new human ones, perming any combination out of 14 altogether.