Professor Andrew Hanson (Indiana University) developed a graphics library for visualizing 4D geometry. It's called GL4D. It's designed to mimic the feel of OpenGL (though I'm not sure whether it is actually built on top of OpenGL). It is GPU-accelerated. It supports projection, slicing, hidden-surface removal, per-voxel lighting, and semi-transparent shading.
Here's the publication which explains GL4D: GL4D paper
Here's a link to the source code: GL4D Source Code
And here's a video demonstration of GL4D: GL4D Video Demonstration