I have two desktop computers at work, but only one desk.
The desktops can sit over on the side, next to the desk, but the real-estate that two monitors would take up is too much to bother with. Also, when I have more than one, I'm always reaching for the wrong mouse, or the wrong keyboard.
Real estate is limited. Location, location, location.
My salvation was a KVM (Keyboard, Video, Mouse) switch. It connects one display, etc., to both my boxes. Installation is instan. It just works.
At work, we use this one. I press scroll-lock (ScrLk) twice, and -- blink! -- I'm using the other machine.
There's a little light on the switch to tell me which machine I'm connected to, but I just use different themes for the different boxes, which makes it immediately obvious. They look different.
I've been very happy with Linksys switches and routers. Their KVM switch works fine for me, but the Amazon reviews say they've died on some folks. Caveat kvm-tor.
I can't cut-and-paste between computers. The sense it gives you is that the boxes are one, so it feels odd that I can't just clip a piece of text, switch to the other box, and paste it.
A web service is an obvious solution: cut text on one machine, paste into another, so long as both are on the web. I thought Control-C would solve my problem, but they don't support Linux yet.
I see references to Synergy, but I haven't tried it. Yet.