1 keyboard, 1 mouse, and several machines

You have 2 screens connected to the same machine, or several computers under different OS. In this post, I present to you methods to make the most of your machines with 1 keyboard and 1 mouse. In other words: switch the mouse / keyboard from your linux PC to the laptop under MS Windows or MACosX, and this in a natural way without special handling. Any self-respecting computer scientist or geek has at least 2 computers at home, or at least 2 screens connected to his machine. »