amakuri

Wow, I had the same idea a while back and thought about writing some kind of engine which does this - but I didn't even begin to research whether someone already did something similar.

Now I see this on HN :)

So I searched and found this: http://www.urticator.net/maze/

It seems to be exactly what you propose, a 4D world rendered into 3D space. It even has a kind of "stereo" mode, enabling a 3D experience on a 2D moniter.

And to expand on the idea: Once we become familiar with 4D, we can continue and use it to explore 5D, can't we?