HaveClip is a cross-platform open-source clipboard synchronisation tool. Set it up and you can copy text or a file to the clipboard on one system (Windows, Mac, Linux), and immediately paste it from another.
There's no installation required - just unzip, and run - but HaveClip does require some manual setup. You must launch the program on every network system where you'd like it to be used, then tell each computer which of the others it'll be accessing. This isn't difficult, really - click Settings > Pool > Add, click "Search local network", select a target system and click "Verify connection" - but it can take a moment.
There are important security considerations, too. Your clipboard may contain very sensitive data, and so HaveClip can encrypt it via SSL or TLS. Again, this isn't difficult to set up - click Settings > Security, choose SSL (for example), click "Generate new private key and certificate" - but you have to ensure all your systems are using the same security settings before the program will work.
(We noticed an odd issue on one computer, where it just seemed to hang at the "Generate new private key..." stage. We waited, and waited, and waited, but nothing happened. Eventually we closed and restarted the program, tried again and it worked fine.)
Once we'd finished the setup process, however, everything ran very smoothly. Almost as soon as we copied data to the clipboard on one system, it was available on another. There was an occasional system lag for a fraction of a second after copying - presumably because of the extra activity in HaveClip launching, and sending the data over the network - but this didn't happen often, and we could learn to live with it.
The program also keeps a clipboard history. Left-clicking its system tray icon displays a menu of the most recent items (10, by default), and clicking any of these copies it back to the clipboard, ready for reuse.
Synchronising the clipboards all the time could be very annoying, of course. You might copy something for your own use, then find it's overwritten because someone else has copied text on their system. Fortunately HaveClip provides options to help: you can tell the program to synchronise manually (clipboard data is only transferred on demand), or set particular systems to send or receive clipboard data only. As you'll only launch HaveClip when you need it, this should probably be enough.