Why can't I stop vim from wrapping my code?

'textwidth' 'tw'        number  (default 0)
                        local to buffer
                        {not in Vi}
        Maximum width of text that is being inserted.  A longer line will be
        broken after white space to get this width.  A zero value disables
        this.  'textwidth' is set to 0 when the 'paste' option is set.  When
        'textwidth' is zero, 'wrapmargin' may be used.  See also
        'formatoptions' and |ins-textwidth|.
        When 'formatexpr' is set it will be used to break the line.
        NOTE: This option is set to 0 when 'compatible' is set.


'wrapmargin' 'wm'       number  (default 0) 
                        local to buffer
        Number of characters from the right window border where wrapping
        starts.  When typing text beyond this limit, an <EOL> will be inserted
        and inserting continues on the next line.
        Options that add a margin, such as 'number' and 'foldcolumn', cause
        the text width to be further reduced.  This is Vi compatible.
        When 'textwidth' is non-zero, this option is not used. 
        See also 'formatoptions' and |ins-textwidth|.  {Vi: works differently
        and less usefully}

If you refer to auto wrapping of long lines sending them to the next one, try

:set textwidth=0 
:set wrapmargin=0

None of the other answers worked for me (IDK why).

:set wrap! Did the trick for me (using GVim for Windows).

set formatoptions-=t should do the trick. set formatoptions+=t will turn auto-wrapping back on.

For more information on what you can do with formatoptions, see the docs.