The Battle for Wesnoth is a Free, turn-based tactical strategy game with a high fantasy theme, featuring both single-player, and online/hotseat multiplayer combat. Fight a desperate battle to reclaim the throne of Wesnoth, or take hand in any number of other adventures. Easily modifiable. You can even download other users' add-ons from the main menu.
Wesnoth is an incredible strategy game with great production values in graphics and music, especially considering it's an open-source project. Some of the built-in campaigns are really top-notch. Multiplayer is also a lot of fun. Modding possibilities are, in a word, fascinating.
The only minor flaws are really in the difficulty levels and balancing. Newbies should experience tons of frustration. Despite all of its great sides, there's just *something* minor lacking in it that would keep me glued to it.
Still, I'd definitely say it's an unmissable game that everyone should try.
Very fun Turn based strategy. I've heard some people complain about randomness but its very controlled and can be planned around. It is also completely open source and has a map editor packaged with it. There are mods people have built to take out randomness too if that's your fancy.