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.
Solidworks - Top end 3D design software
Education in 3D Site - Repository of .stl files and lesson plans grouped by subject area
Tinkerine U Lessons - Great lesson ideas for art, math, science and more
SeeMeEducate 3D Printing Curriculum - Many great links/foundation for getting started with 3D printing with students
Autodesk Workshops - Try filtering by "STEAM" projects if you want to cut down the number of options
3D Printing in School - An open source curriculum
Invent To Learn Guide (Book)