Global Context Menu

I know pretty much nothing about the windowing system, so this might be a dumb question, but how are context menu's handled? Is it possible to access say, Google Chrome's context menu from a desktop application?

Is it possible to create a context menu that shows up when you right click no matter what application has the "focus".

I ask because I am interested in creating some options that I can tack onto a context menu of any program that allow you to modify the contents of the system clipboard and would be useful no matter what you are doing.

If the above is not possible is it possible instead to override an applications right click action with my, global context menu?