Vim (installed as vi by default in some Linux distributions) — A modern vi work-alike with more features, including a scripting interface for Perl, Python, Ruby, Tcl and Scheme.
nvi (installed as vi by default in BSD operating systems and some Linux distributions) — A free replacement for the original vi which maintains compatibility while adding some new features.
vi (default under Unix — unless replaced by a vi-clone) — One of the earliest screen-based editors, available in Unix, and part of the POSIX standard. Vi is based on ex.
SETEDIT — a clone of the editor of Borland's Turbo* IDEs
vile — A vi work-alike which retains the vi command-set while adding aspects of the Emacs editing paradigm: multiple windows and buffers, infinite undo, colorization, scriptable expansion capabilities, etc.
mcedit — Full featured terminal text editor for Unix-like systems.
TECO — One of the most advanced character-based editors, which included a programming language. While usually described as a line editor, it included screen editing capabilities at least as early as 1965.
NED (text editor) — The Rand fullscreen text editor, also known as re. A white-space editor, allowing arbitrary cursor movement past end-of-line or the last character of the file. Small amount of integration with the MH mail system.