I do most of my work (embedded development) ssh'd into a few linux boxen at the office which can reach my test devices and various other bits and bobs.

I'm pretty happy running full text mode editing in emacs (-nw, ftw :) and a few other shells for tasks I haven't incorporated into emacs yet. Speed is nice, even over a vpn, which running anything graphical is somewhat grim.

Still, the killer feature with screen multiplexers (in my case, tmux, but this isn't unique to tmux) for me is the fact that the tools preserve state, so I can start a long job and it won't be interrupted, even if the connection drops. I just log back in and reattach and everything is just like it was.

Sure there are other ways to do that, but having it neatly wrapped up and always on is really a game-changer for me.