Okay, this is lame - no posts since December... Hopefully this will make up for it.
I've been spending a lot of time lately researching 3D animation for a project I'm working on, and I'm drawing a line in the sand for ease of reference, later. Hopefully, someone out there will find it useful.
Blender has been my tool of choice, because it's easy to find documentation and samples out on the web (plus, it's FREE). Of course, 3D Studio Max is a professional (expensive) program which provides the same functionality - probably more. It seems to be one of the more popular options, based on what I've seen while trolling the internet.
Blender
Let's start with Blender stuff... At a high-level, Blender is the 3D modeling tool. You start off with basic shapes (sphere, cube, etc.), and deform those like working with clay. You can then pose those models and create a series of animation frames.
I highly recommend checking out the gallery page on Blender's website. This will give you an idea of what the product is capable of. The lighthouse movie is particularly cool... :)
Here's an excellent site with quick-start video tutorials. Spend 1/2 day running through the first few demos, and you'll have a good handle on Blender and 3D modeling (maybe less time for you artsy folks).
Last, here is a quick video tutorial on something called "rigging." Rigging is the art of adding movable bones to your models, so that you can animate them. This is the key to building moveable models. There are more detailed tutorials available on the site above, but I like this one because it's very short and sweet...