
http://www.blender.org/
It also has a portable/standalone version, and there are usually portable versions available here:
http://portableapps.com/search/node/blender
Blender is probably THE most popular free 3d modeling app available. The main thing I like about Blender is that it is free.

But, there are other free 3d apps, but the thing that really sets Blender apart is the HUGE community. There are dozens of places to get support, including various forums (official and unofficial), a "newsletter," tutorial sites, and youtube vids.
It is fully featured. In addition to the 3d modeling part, it also has animation editing/rigging, a basic game engine and some basic compositing features. In fact, I only have a vague idea of all the other things it can do, since I don't get much deeper than the 3d modeling part.
Here's a link to a "box" modeling tutorial I did a long time ago for Blender, of a shotgun:
http://lowpolycoop.com/forum/viewtopic.php?t=73
Another tutorial on transparency:
http://lowpolycoop.com/forum/viewtopic.php?t=75
And another on UV mapping in Blender:
http://lowpolycoop.com/forum/viewtopic.php?t=74
(Note, some of these might not be quite right now, as those were ~ 3 years ago. Holy CRAP I can't believe it has been that long.....)
It shows that you can, in a relatively short amount of time, start modeling some fairly complicated designs.
I also like the plugins. It can import/export just about any format, and there are enough Blender-folks around that if there is a need for something, someone somewhere will be working on a plugin for it.
Here are some disadvantages I have seen people complain about:
- Lack of focus. As all of us here know

- Lack of cross-over. The Blender interface is.... unique. It relies on keystrokes ALOT, and the whole paradigm for how it does things is different from the big retail 3d modeling suites. So, if you learn on one of those, it might be difficult to go to Blender. And, if you learn on Blender, it may be difficult to switch to anything else. Also, I have heard that it is not tablet-friendly. It will work with a tablet, but not as well as some other payware apps.
So, I hope that is the kind of thing you're looking for, SnakeMan.
