Today I finally took some time to fix a long-standing problem: when trying to edit a file on a remote host using Emacs tramp mode, long time-outs occurred when typing the remote file name (after hitting C-x C-f). These time-outs were so long and occurred after each key press that tramp was effectively useless.
After some digging (e.g. excluding helm as the problem source) I found this entry in the Emacs Wiki which basically told my that using zsh (the Z shell) on the remote host could be the culprit. Indeed, after adding
[[ $TERM == "dumb" ]] && unsetopt zle && PS1='$ ' && return
at the top of my ~/.zshrc file solved the problem instantly. What this line does is simply replacing the shell prompt with a very simple one (a $ followed by a space) if the terminal is of the dumb type (which is the case for tramp).