After upgrading to Ubuntu 13.10 some time ago I noticed that my compose key (i.e. the key that you press followed by e.g. c and , to create a ç) didn’t work anymore in Emacs. I found two bug reports on this issue [1, 2], both effectively suggesting the same solution: start Emacs like this

XMODIFIERS=@im=none emacs

So I added the following line to my ~/.zshrc and ~/.bashrc files:

alias emacs='XMODIFIERS=@im=none emacs'

(of course somewhere before I set my EDITOR variable). I also changed the command in the launcher I use (GLX-Dock/Cairo-Dock).
This doesn’t make it a system-wide (or even user-wide) fix, e.g. the Firefox add-on “It’s all text” doesn’t get it, but it covers most of my use cases.