Arkanoid
When I got my FPGA board in 2007 (this Xilinx Spartan 3E board), I needed a project to work on - something 'appealing'. The fact that the board had a VGA port hooked up to the FPGA made me decide that I wanted to make a game, and Arkanoid/Breakout it became.
The game was designed in hardware only, no software is loaded into a microprocessor. The paddle board could be controlled by means of 2 buttons on the FPGA board. When my prototype with 9 bricks worked, I stopped developing the game. All VHDL source code can be downloaded though.
A video of the prototype is shown below.
In 2008, Roberto Schiabel from Italy contacted me that he wanted to port the design to work with another FPGA board, and adding support for a mouse as user input. He finished this, and made the source code available. More can be read on his blog.