I finally got around to trying out John McIntosh's 4D Blocks game, and I have to say, I'm awestruck.
This game begins with a 4D maze to acquiant you with the movement controls, and then you can load in other world description files that lets you explore 4D (and 3D) worlds in first-person perspective. You can pick up blocks, move them around, and use them to build larger structures, and there's even a cute little animated train that moves around preset tracks, that you can try to follow around in 4D to see how good your 4D tracking skills are. The game comes with 400 different scene files that you can load, and includes all sorts of scenarios, from mazes to city blocks to train loops, there's even a couple of files that lets you play with a 120-cell in-world (i.e., as a real 4D object that you can pick up and move around, or look at from different angles -- not just an isolated object but part of a larger world). Really amazing!!
It does take a while to get used to the movement controls and the perspective projection 4D view, and the graphics may look primitive at first glance, but don't be fooled! Once you get used to it, you feel like you're really living in a 4D world! Very highly recommended way to explore a truly 4D world! It will truly test your ability to visualize 4D and develop a real geometric intuition for 4D space. I cannot recommend this game enough! Stop reading this and go download and play it already!