In an 80 column wide terminal emacs wraps 80 column lines, putting a backslash in the 80th column. Is there a way to tell emacs to use all 80 columns of my terminal and not wrap lines until they reach 81 characters?
If I understand this question correctly, this is not about logical line wrapping (how lines are segmented in your file), but about visual wrapping (how lines are displayed with respect to window width).
If you just want the display to visually wrap more than zero characters before window boundary, and thus avoid the backslash everywhere, however long your logical lines really are, you can use longlines-mode :
Unlike Visual Line mode, Long Lines mode breaks long lines at the fill column (see Fill Commands), rather than the right window edge. To enable Long Lines mode, type M-x longlines-mode. If the text is full of long lines, this also immediately “wraps” them all.
Then, it's only a matter of setting the fill-column appropriately, using
either global settings (.emacs, though you probably want to use a
specific mode-hook for that particular case), local settings (file
variable, dir-locals) or C-u 79 C-uC-x
f to set variable fill-column to 79. This way, lines 79
characters or higher will wrap, but before touching the right edge of the
80-char window (and thus never leaving an ugly backslash character). Your
file will be untouched.
If you simply want no visual wrapping to occur on 80-character lines, and thus do not want the 80th logical character visually displayed below the first, there are two possible answers:
either you work in an environment where you don't necessarily wrap logically at or before 80 characters, and you want to see the end of those 81+ lines somewhere in your screen (i.e. you do want visual wrap, but at a number of chars above the window width), then I don't know how to do it.
or you want to stop your lines at 80 chars logically (e.g. you
have auto-fill on and fill-column at 80), and if you do happen to have
lines 81 characters or more, you don't care about seeing their ending.
In that case, activate truncate-mode (toggle-truncate-lines).
If the issue is about the last character of your window, and what you really want is the 80th logical character of your line to be displayed on the 80th visual character of your window, though, I'm afraid I don't know how. Either you are truncating lines (as above), and the last character of your window will be a $, or you let emacs do its thing, and the last character will be a backslash.
Note when testing that auto-fill's wrapping (but also longlines-mode's, since it is its visual equivalent) will occur only at word boundaries.