Blender is a really amazing free and open source 3D modeling application. You can use Blender for animation, rigging, sculpting, games and even video editing. You can use Blender for commercial purposes, and it is not restricted as some applications are. There are extensive tutorials to get you started here.
There is a Blender manual and also a large lively community where you can get help. This is a recent example of an interior art project done with Blender. This incredible 3D model portrait is done in Blender. The Blender Foundation makes movies showcasing the capabilities of the software. The latest one Tears of Steel is here. The movies and the software are all made by volunteers and completely open source.
Blender is also a great tool for 3D printing. Shapeways has a tutorial on Blender and 3D printing as does Sculpteo. One of the many Blender extensions is 3D printing toolbox which has specifically been made for 3D printing. We want to make 3D printing easier for all and love Blender! Free open source tools are a great way to make 3D printing accessible. Due to this belief, we made a Blender Plugin.
You can find the Blender plug in here. We’ve made a handy little video on how to install the Blender plugin. By using the plugin you can quickly prepare and repair your 3D printing files. Please do give us feedback on the Blender plugin!