Freeciv 'cause civilization should be free or so it says when it starts. Freeciv is basically a free, open source version of the strategy classic Civilization 2. It has a few differences, or so I'm told, never having played Civilization. It is however a superb game in it's own right. The game supports multiple computer and human players in a complex and rich world of alliances, trades, and battles. Your aim: to get a spaceship to Alpha Centauri before any one else, without them killing you first. There are two approaches, the outright war, and the speedy researcher. Generally I use a balance of both, but feel free to try out your own style.
It's a really complex game engine, the chances of you winning a battle depend on hit points, attack strength etc. but also terrain, and even your type of government can affect how your military units work. You start from stone age technology with warriors (with big sticks) and settlers (who build towns) and you gradually progress through to having space vehicles. The map you live on is nominally an entire planet, although this can be altered so that it represents just a small area of a planet's surface. This also points out another great strength, there are a vast array of options and settings you can set before you start.
Best of all, it's free! And due to the fact that version 2.0.7 is now readily available for Windows, you can all enjoy it without upgrading your operating system. It also allows for network and internet play, it's not a demanding game either. If you're intending on having a big network game with lots of players on a big map, I would suggest having someone with a fast computer host any AI players, other than that, if the computer is above about 300MHz it should work just fine, and if you're computer isn't faster than that by now, let's face it you ought to think about using it as a book end.