"Battle for Wesnoth is one of the most popular turn-based
strategy games for Linux, if not the most popular. Completely free
and open-source, it provides both singleplayer campaigns, as well
as online multiplayer, hotseat or LAN support. The game takes place
over various maps composed from hexes, and in each hex a unit at a
time can be deployed. The player has to take advantage of various
terrain types (which increase of decrease defence), use wisely the
types of attack and abilities each unit has. Wesnoth currently
comes with 5 factions (Loyalists, Rebels, Knalgan Alliance, Undead
and Drakes), but the add-on server has a whole bunch of custom eras
and new factions.
"SuperTux is a 2D jump and run Mario clone, with the difference
that it uses its own maps, enemies, and the main character is...
you guessed, Tux, the story taking place in Antarctica. It is
licensed under the GPL and it is free of charge. SuperTux has very
nice graphics, especially since it has support for software and
OpenGL rendering, 26 levels and 9 types of enemies."