Okay, the title is slightly misleading ..
You can not move layers without touching them, but you can move them from the layers palette without clicking on them using the following keyboard shortcuts:
To move a layer down to the layers palette, press: Command-left bracket (PC: Ctrl-left bracket)
To move a layer to the palette of layers, press: Command-right bracket (PC: Ctrl-right bracket)
Now, if …

You are probably already familiar with the History of Photoshop, which allows you to undo up to 20 steps. Unfortunately, when you quit Photoshop nothing is saved in memory and this no longer works. However, there is a way to undo changes to color and tone after days, weeks or even months.
Here is how: next time you apply a change …