(Blender Foundation) is a free 3D studio for animation, modeling, rendering, and texturing offering a feature set comparable to high end and mid range 3d animation suites such as Maya, 3ds Max, or Cinema 4D. It includes advanced features such as multiresolution sculpting; retopology painting; 3D view texture painting; stack based modifier system; advanced particle system with particle based hair; cloth/softbody dynamics, hardbody dynamics and fluid simulation; node based texturing and node based compositing; an integrated non linear video editor; and integrated game engine. Blender is developed under the GPL and runs on all major platforms including Windows, OS X, Linux, BSD, Sun, and Irix. It is also the only 3D animation suite that is flexible enough to have been scaled upwards to work on super computers but also scaled down to work on handheld computers such as the Pocket PC (Pocket Blender). Blender has a unique interface which can make it hard to start learning. To see what Blender can do take a look at Elephants Dream and Big Buck Bunny.

Elephants Dream from Blender Foundation on Vimeo.

Big Buck Bunny from Blender Foundation on Vimeo.

Here is a chart that does a fair job comparing 3D software programs. Note that it is a few years old.
Get Blender:
There are currently two versions of Blender available right now (March 2010). There is version 2.49 which is the latest stable version of Blender that utilizes the original user interface that most/all tutorials and books reference. There is also an alpha version 2.5 that aims to shift Blender from an intimidating and unorganized interface into a more polished and welcoming professional tool. This version is still a little buggy and is missing some tools and functionality but should be fully functional by the end of this year.
Learn Blender:
Part of the beauty of Blender is the huge community of users that support it. There are countless websites, blogs, and tutorials devoted to Blender.
The Blender Foundation has a number of tutorials that will get you started using this program:
There are a few video tutorials on the foundation website that will show you some of the basics and may better demonstrate the nuances of the user interface better than static pictures and text.
The site also has an extensive wiki that covers everything in detail.
Most tutorial videos are hosted by Youtube so it has become a very good resource for learning how to do just about anything with Blender.
Blender has a pretty good renderer included but it also works well with another free open-source software called Yafaray. It can be a little tricky setting it up properly but can yield excellent results.
There are now quite a few books available that will help you learn Blender, each one covering a different aspect of this powerful program. While the tutorials can get you part of the way the books offer a more polished and professional approach to learning the program.
The Essential Blender: Guide to 3D Creation with the Open Source Suite Blender by Roland Hess is a good introduction but doesn’t get you much further than the free tutorials online. Save your money and get one of the more specific books once you have mastered the basics.
Tony Mullen is writing the most useful books about Blender,  each one devoted to a specific aspect
Mastering Blender
Introducing Character Animation with Blender there are two versions of this book the one below just came out and uses version 2.5
Introducing Character Animation with Blender
Bounce, Tumble, and Splash!: Simulating the Physical World with Blender 3D
Blender Studio Projects: The Open-Source Animation Pipeline
Blogs and Websites: Great list of Blender affiliated websites The name says it all Community blog about all things Blender Okay collection of Blender models Includes a number of higher level tutorials that are pretty good. Focuses on using Blender for architecture visualization Tutorial website
Extend Blender with Plugins:
1.Hynds|Studio Blender Fur Library Volume 1
Great collection of animal fur
2.Meta’s Materials Library’s
Nice materials collection
Add a gear to your primitives
4.Create Bolt_Thread
Create bolt threads with ease.
5.Julia Fractals
Generate  complex fractals.
6.Hand Writing Tool
Draws extrusion of a selected mesh.
Generate 3D, mesh based, trees.
8.Cloud Generator
Volumetric clouds have never been simpler.
Create simple people models.
10.Blender People
Really cool animation script similar to Massive.
11. Blender Plugin Repository
Some of this is quite old and may not be useful
This is just a small list of the add ons you can download for Blender.