Blender

Highly Recommended

Blender is an open source 3D content creation application. Stuffed with features, and with an enormous user base, it’s one of the most supported and best open source programs out there. The learning curve can be steep, but with time and close attention to the thousands of tutorials available, it’s everything a hobbyist 3D designer could want. It is available for Windows, Linux, and Mac.

Blender Website

BlenderArtists Forum

Blend Swap - User created models, materials, and more, under a variety of licenses.

Blender Wiki

Competition

Unity

What It's For

An all around 3D modeling package for everything from making models, animating, creating games, and rendering. It can be used to create models and animations for games, or it can be used to create animated movies or still renders of any kind.