3D Graphics on Linux

Modellers

AC3D
Easy to use 3D modeller with a simple model format making it easy to load the models in your own applications.
Cross platform well at least Linux and Windows (MAC version is currently (2005) in beta testing).
However it is NOT FREE but at $50 it is't expensive either. I actually bought a licence and I'm quite happy with it.

Innovation3D
Interesting FREE modeller, has Debian packages and modules for handling AC3D models.
I defiantly have to give it a try some time.

Vertex
One of the first "modellers" I tried on Linux, somewhat hard to use back then (vertex movement by modifying coordinates) don't know if the UI has improved since then. At least it is free.

Blender
Free cross platform modeller, took me quite some time to get used to when I tried it. Haven't tried to load its models. One interesting feature is the possibility to export to VRML models.


Programming

3D programs are't that hard to write... Now get coding you lazy bastard.

I highly recommend that you use OpenGL a cross platform 3D library, unlike DirectX used by some programmers on certain "game consoles".
I also recommend the usage of some cross platform library to open the window containing the 3D graphics, after all who wants to write software that can only be used on one operating-system?
I recommend SDL for games, and WxWidgets for applications.

Tutorials and documentation

OpenGL basic function reference
Lots of OpenGL tutorials
Apart from this there are lots of stuff on the Internet.