Honest question: Is there any benefit of using tmux over a proper tiling window manager? Or, why would I want to delegate some of the window manager tasks to a terminal emulator?
I use both a tiling window manager (xmonad) and tmux. The main reason I started using tmux was to do pair programming sharing the same terminal via ssh. If you pair program and have never tried this before, I highly recommend trying it. I live in Japan and even pair with people in London using tmux and vim. It's the next best thing to being there.
After I started getting used to using tmux, I found that my workflow naturally separated between things I'm doing on my terminal and things that require X (like my browser). These days I use a separate workspace for X apps and terminal (occasionally moving them around).
To make my life easy, I've added xmonad-like key bindings and window layout to tmux. Since other people are sharing:
I often work while travelling and when I'm on the road I often don't bother cranking up X -- just work in the Linux console. Using tmux I barely notice a difference in my workflow and it helps extend the battery.
For me it's having two different terminals connected to same tmux session. I use tiling window manager and work on two monitors. Sometimes there is some stuff that I'm working on on my main monitor but I want to have quick look at the terminal. Because I have two terminals opened on both monitors I can just switch to the other one, press ctrl+f(my prefix)+number and have exactly same window as in my main terminal.
For anyone wondering you can achieve above by typing tmux new-session -t and giving it number/name of your current session.
Also there are minor things that are nice. Like if you need to open another terminal instance in the same directory as you're currently in.