dipos can save and restore your desktop icon positions. It is a single small executable without the need of an installer. Just run the application to save your dekstop layout to a file. Drag and drop that file on the executable to restore your icons.
Please download the 64-bit version of dipos if you are running a 64-bit windows!
I would bet that this is the best application that does the saving and restoring of icon positions. It's small, fast, runs from a flash drive, has the 64bit version, it's free, hmm what could I want more? Ah yeah, I want to have shortcuts for different positions schema. Well it does that too: call the application with the desired .dip file and it will load that file without having to click on some GUI menus.