Battle for Wesnoth is a turn base strategy game where you have to wait for the other players to do their turn than can do yours. Its Gameplay is based on the more famous "Heroes of Might and Magic".
In this screenshot you see yourself (figures with red) in a complex fight against two opponents (black and green). The black figure above the castle tried to attack your figure inside the castle and lost 3 HP.
The game is quite complex and to play the tutorial game before actual games is highly recommended. (Units gain advantage due to terrain, day/night, leadership, magic, etc.)
You can play this as hot-seat multiplayer game because everybody takes their turns after another anyway.
If you play this via network you also have to wait for the others to make their turn.
It has full game documentation here, but I've never read much of this site, can't tell how it is.
Wesnoth is FOSS software.
Liquid war is a very special game (not turn based, but matching the other criteria). You control a pointer where your Liquid tries to get to. You should control this via mouse, but can do it with keyboard as well. It supports multiple of each. When the liquids of two players meet they start to consume each other. So, you need to "surround" you opponent while at the same time ensure that no place of "you" is too thin for you opponent to break through.
It supports hot seat and as of version 6 network game.
The core concept is easy, but this game can be very challenging.
In this screenshot you see red and purple being at war quite intense while blue tries to reach the action.