TinkerCAD - This is a very easy to use and intuitive site for designing objects. TinkerCAD was acquired by Autodesk, so the account you create for TinkerCAD will also work for Autodesk products. Educational access available for account creation - contact Jason Martin-Hiner for details.
123D Design - A program similar to TinkerCAD, but offers more high end design options. In browser and downloadable option.
123D Sculpt - Looking to work with digital clay to create more organic models? 123D Sculpt may be for you
3DTin - Another simple, in-browser, design program.
Sketchup - Iowa educators have the opportunity to use this full-featured program for free. Contact Vic Jaras for details
Solidworks - Top end 3D design software