I have Illustrator CS6 on my laptop and my PC, and I do work on both of them. Is there any way to have the two computers automatically share the same user defined swatches that I create? I do not like having to copy the swatch files from one computer to the other. Both are running Windows 7 and they are networked wirelessly.
Nope, not from within the Adobe apps. You will have to use some externalf file syncing tool.
You could create a template file that contains all of your swatches (and brushes and styles, for that matter), then save the .ait to DropBox or other cloud service. Then when you use it to create a new document, your swatches will be there.