If you're running a modern Linux desktop, you should have a "notify-send" command which will cause a message to be displayed by your desktop-environment's pop-up notification system (on Ubuntu, this command is in the libnotify-bin package). I have two scripts I keep around which I call "notify-success" and "notify-failure":
With tmux, you can monitor the window for activity (^A M) and do:
make -j3 >make.log 2>&1 ; echo $?
When make finishes, your prompt is printed again (activity!) and the window's caption is highlighted. I use the same mechanism to watch for new mail and chats in other windows. It's like Growl for your terminal.
My terminal (urxvt) will detect the bell and set the 'urgent' flag on the window, which is detected by Awesome, which sets the appropriate tag* icon to red.
* Tag in Awesome is more or less akin to a virtual desktop.
I just use a few aliased beep sequences so I can have an audio notification. I never have much need for more than a few at a time, so I've only written three such aliased beep tunes. Well, four really, I always have a special keyboard shortcut set to immediately run the one named "little_melody". By pressing down... well you get the idea.
notify-success:
notify-failure: When I want to run a long-running command and don't want to have to keep checking on it, I'll do something like this: