Most of my FPGA designs have been for industrial purposes, such as processing signals and controling hardware. I haven't really used an FPGA in a truly interactive way. I got the idea to create a video game on an FPGA right before a long business trip to China. I knew I would be spending long hours on an airplane and in a Chinese factory and needed something more productive that watching TV in my hotel room when I wasn't in the factory.
You can see the code on Github. Look in the rtl folder to see my Verilog code. I am directly driving the 5 VGA pins (RGB, Vsync, Hsync) with digital outputs on the Cyclone IV FPGA. A reistive divider is used to lower the 3.3 V outputs to the appropriate VGA voltage levels for the red, green, and blue channels. The digital Vsync and Hsync control signals which are spec'ed at 5 V work just fine at 3.3 V. Player position is controled by a mechanical encoder driving two digital inputs with internal pullup resistors.
Here is a short video of my game in action: