I recently started on my GBA mission: to boldly go where I've never gone before, the realm of games and console programming. To start the mission, I began attempting to make a port of Sokoban, which is now complete.
My plan is to keep increasing the difficulty of the games I'm working on until I reach the point where I'm incapable of creating something better. Once I'm comfortable with GBA programming, I'll look into DS programming.
I've only created Sokoban so far, but more, well at least one is on the way.
In order to play Gameboy Advance games on your PC, you need an emulator (which emulates the Gameboy Advance hardware).
The two most popular emulators are:
Either of these can play the games I have made.
If you want to get into GBA development yourself, you need specific compilers and tools, here are a few links to get you started: