Stroids3D
Stroids3d started out as a 2d clone of the original asteroids. Since I have no life and just a horrible amount of time on my hands, it eventually became a full 3d space shooter.
About
"It started out just like the original (2D), but then he made your ship and all the asteroids 3D (but still stuck in a plane like before). Then he changed it to a first person perspective and made it so you can look and fly in any direction. Now, it's really nothing like asteroids, but it's still really cool."
--John Bethencourt

John Bethencourt has a very nice description and some screenshots showing off the Non-Euclidian asteroids idea that he implemented into the game.

Stoids3d was written using OpenGL and SDL . It currently runs on Mac OS X, Windows, and Linux.
Stroids is released under the GPL.

Download
Here is the lastest compiled version: Stroids3d v0.9 Windows
Source Code
ViewCVS may be down. You can get the source on the downloads page.
The easiest way you can look at the stroids3d source code is with viewcvs
http://www.upl.cs.wisc.edu/cgi-bin/viewcvs.cgi/stroids3d/
Stroids3d is not finished but you can still try to compile it if you want.
You can grab the source out of cvs. It is released under the GPL license.
VC6 and MacOS X project files are usually behind so you will most likely have to add source files to compile with those tools.
The VC2003 project files are the most up to date. The linux make file is usually not far behind.
ScreenShots
Credits
Programming:
Tony Magro
John Bethencourt
Nate Griswold
Art:
Tony Magro
Ship model by Ghoulish Arts
http://ghoul.flipcode.com