In Terminal, type this:
pbpaste | ssh user@hostname 'pbcopy'
Alternatively, I might want to keep the text in a file on the distant computer. This works for that purpose:
pbpaste | ssh user@hostname 'cat > ~/file_name.txt'
[robg adds: For true clipboard sharing between machines, I'm partial to PTHPasteboard Pro, whichh makes it simple to keep two or more machine's clipboards in sync -- text and graphics are both handled with ease. There are numerous other solutions out there, too, such as DropCopy (which is also very useful for transferring files).]

