In addition to downloading free 3D models from Thingiverse for 3D printing, you can create your own!
Here are a few free 3D modeling apps:
SketchUp was previously a Google project that is now owned by Trimble. It is an easy-to-use app for creating 3D models, but does require a plug-in in order to export STL files for a 3D printer.
123D by Autodesk:
A suite of several different browser-based applications for 3D modeling using various methods such as converting photos, building 3D from 2D slices, and combining shapes. Requires browsers with WebGL support.
An open source application that can create professional level modeling and animations, but with a steeper learning curve. Able to natively export STL files for 3D printing.