3D Rendering and Animation
POV-RAY http://www.povray.org
Free-source available but restricted. Windows,Mac or Linux/Unix
Was once the most widely used free renderer on the planet. Script based and very flexable but very difficult to master. Creation of complex shapes requires the use of a 3rd party modeler, unless you have the brain of a supercomputer. Great for abstracts though.
Wings3D http://www.wings3d.com
Free-open source. Windows, Mac OSX or Linux
Extrusion box modeler, useful in conjunction with POV-Ray. Easy to use but no rendering or animation support, a dedicated model-making program.
Anim8or http://www.anim8or.com
Free. Windows
Basic modeler and animating package. Relatively easy to use but not widely used for much outside the Anim8tor community.
Blender http://www.blender.org
Free open-source. Windows, Linux/unix and Mac
Full modeling, animation and rendering package. Somewhat hard to learn but reasonably powerful. Recently open-sourced, so expect upgrades and plugins to start rolling in to increase usability.
Truespace 3D http://www.caligari.com
Cost varies by version, older versions given away free
An older package but still with many adherents. The rendering engine can't touch the top packages, but for free it's fine. Objects not as commonly available as they used to be, but still plenty out there for the finding.
Lightwave 3D http://www.newtek.com
$1000 to $2000, Windows, Mac, Linux
Professional broadcast-quality 3D modeling, animation and rendering tool. Extensively used for TV and movie VFX. Expensive but very powerful and reasonably easy to use. Fast renderering but with poor character animation support, although third-party plugins are curing this. Substantial student discounts available, and a free restricted-use 'learning edition' demo is available.
3DStudio MAX http://www.discreet.com/
$500 upwards, Windows.
Professional-quality 3D modeling, animation and rendering tool. Extensively used in the games industry and by hobbyists. Not regarded as good enough for broadcast or movie VFX use without an add-on rendering plugin. File formats not readily portable to other tools, and is a bit of a resource hog. Considered somewhat unstable and difficult to use when compared to Lightwave or Maya. A dedicated cut-down version called G-Max for games modelling is now freely available.
Maya http://www.aliaswavefront.com
$1500 to $17000+ WIndows, Mac, Linux
The Premier 3D modeling, animation and rendering package. Used for many movie VFX, but the full version sells for $17,000! Cheaper versions and demos are available for substantially less, but have accordingly smaller feature sets. Considered by many as the state of the art for 3D tools, superb for character animation but the rendering engine is knocked by some. Many VFX companies build and animate in Maya, then do the final rendering in Lightwave or a custom engine instead.