Advance Wars is an excellent turn based strategy game for the Game Boy Advance. It was developed by Nintendo and Intelligent Systems. If I recall correctly, it is the latest game in a series of (Insert Nintendo system here) Wars games.
The basic idea is to command your force of soldiers, tanks, aircraft and naval craft to destroy your opponent's units and or capture their headquarters. You have a wide variety of troops at your disposal - from your average, everyday soldiers who can capture facilities for your use to mighty Medium Tanks which can crush any other land-based units in close combat.
One of the unique twists in this game are the Commanding Officer Powers (hereafter known as "CO Powers"). Basically, each of the CO's have their own unique abilities that will effect your units in combat. For instance, Max's tanks are much stronger than any other character's tanks, and his ability will increase their powers even further. Meanwhile, Olaf can create a snowstorm, during which his troops can move much farther.
The game includes several modes, including a single-player Campaign mode, a Versus mode where you and up to three other players can pass a single unit around blowing each other up, and a Map Design mode, in which you can create your own battlefields.