You could run emacs on the remote machine. Emacs runs in a text terminal with only a few minor snags (mainly some key combinations may not be recognized, e.g., C-S-letter may be seen as C-letter; this is due to the terminal emulator). If you frequently connect and disconnect to the remote machine and want to avoid emacs's relatively long startup time, run it under screen (start
screen emacs; before you disconnect, type
C-a d; when you reconnect, type
If installing emacs on the remote machine is a problem (e.g., on a computer with very little disk space), there are a few small editors with emacs-like keybindings, such as
jmacs (a configuration of
zile. However they tend not to feel very emacs-like, because most of emacs's power is in its hundreds of lisp packages.
But the option I'd recommend is to keep running emacs locally, and to use some method of editing remote files. Emacs has a native method for editing files over ssh: enter the file name as
/mysite.example.com:/name/of/remote/file. This is documented under “remote files” in the emacs 23 manual, and in the separate Tramp manual for older versions of emacs.