My first foray into 3D modeling and animation was this past weekend, so by no means do I consider myself an expert on the subject. What I can do is tell you what I have found so far, and promise you that the journey will continue and I will happily post good tutorials and reference materials for the tools I am about to describe.
I was looking into software that would help me do modeling of buildingsso I could have fun planning out the secret passageways of my dream fortress. Combine that with my being an avid Linux user, and I stumbled across Blender. Blender is a very complex and powerful tool, and you can do much more than model buildings with ityou can model anything you want. However, one of the first things I figured out was, it’s hard! On the bright side, it is free, and as it is open-source, you can contribute to the Blender’s development, modify it, and program it to your heart’s content: Blender is written in C, C++, and Python (Yay!).
When you get into 3D, what is stopping you from 3D animation?! After Eli’s articles on video production and editing, Rick (President of Eduporium) introduced the team to Source Filmmakeran animated video tool created by Valve Corporation (the major gaming company). Source Filmmaker is built upon the Source gaming engine, which means that you can create videos while being inside a virtual world. Also, you can change how characters move, talk, interact etc. while still being able to 1) see what the final product would look like, 2) position virtual cameras in different locations of your virtual scene and “shoot” from there. 
Source Filmmaker is in beta and, therefore, has a thematically limited amount of pre-loaded scenes (or “maps”), players, and propscurrently these are imported from Team Fortress 2. Now if you don’t want to have scenes in concrete buildings or animations that involve explosions that’s where the 3D modeling comes in. It is possible, albeit difficult, to make your own scenes, characters, animations and props that you can then import into Source Filmmaker and make videos of these. Blender, with a few added plugins, has everything you need.