Learning vim was valuable for me since many servers that I manage have it installed, so it's easy to edit files on them. For example advanced searches using regex (and replacing), multiline editing, jumping to function definitions etc.

For servers that don't, they usually have vi at the very least. (i.e. BusyBox)

As for emacs, I've been interested in trying it before but it seemed to require a separate graphical application? But I could be wrong.