I do 3D art off and on. A great starter program is Bryce, which is used for rendering 3D scenery. It has a terrain editor, sky editor, tree editor, and even animation capabilities. Version 5 is out and you can buy it online from Daz3d. It was around 200$ US if I remember. You can also make simple models with boolean procedures.
Vue Esprit 5 comes out soon and is another scenery rendering program. It is competetive with Bryce.
Poser is used for creating and posing human and animal models with clothing, props, and settings. Poser 5 has animation capabilities, as well, and the hair editor is new in version 5.
The high end programs are 3D Studio Max by Discreet, Lightwave 3D by Newtek, and Maya by Alias|Wavefront. Maya is around 10K$ US, 3D Studio Max was around 3K$ and Lightwave was around 1K$. Rhinoceros is a newer concept and started out as just a 3D modeler. Lots of add-ons have been created for it though. It is a LOT easier to learn than the others.
There are some free ones, but they fall short in several areas. Those include POV-Ray, Spatch, Anim8tor, etc. Just do a Google search for 'free 3d software'.
For really cool anime style mecha and spaceships, you can try DOGA L1. It is Japanese and you'll have to sift through their website. Sorry I can't post links yet.
Also, 3D text models can be created with Elefont. I don't know if it is still free, but it uses your built-in true-type fonts to create 3D models out of any words you type in and you can manipulate them with bevels, depth, etc. Really useful!
A great web resource for 3D art is Renderosity.com and also Daz3d.com
They have a lot of stuff, but be warned that a lot of pagans post a lot of pornography that they call 'art' in their galleries, so put on your filters.
My galleries have 3d art on them at Annihicorp.com - but be warned, that was before I gave myself over and some things are not quite Christian on there. I have to get to editing all that, so be warned.
I hope this helps!
Lael