Blender -- open source, free 3D animation system

blender: Open-Source, Free Software: 3D modeling & animation tool with advanced features such as a non-linear animation mixer.
Lots of scripts are available for translating between other 3D applications.

Note for those running XP with an ATI video card:
While ATI has optimized 3D, they've broken some 2D features in recent (2005) OpenGL library. This may impact Blender's UI performance.
EASY FIX: Upgrade to latest Catalyst driver but then extract just the OpenGL .DLL file from a known working version such as Catalyst v3.9 to put in Blender's folder.
elYsiun Blender user community: Lots of helpful tutorials and shortest-path to achieving tasks such as:
Extrude object along pre-defined path
Join objects and remove double vertices
Snap to grid while translating (scaling, rotating)
The Gimp: The GNU Image Manipulation Program. (You might not need photoshop after all!)
YafRay: A powerful render engine (supported by Blender)
POV ray ray tracing engine: One of the best and most popular renderers in the world.
There is a script to export Blender scenes for it.
Renderman-compliant engines: open-source: Aqsis, Pixie; Closed-source: 3delight.
Excellent Whale's Blender HotKeys: Quick reference for keystroke sequences, indexed by key and function. Also includes links to downloadable keyboard map.
Blender keyboard poster from Estonian Academy Of Arts