I’ve encountered a weird little use case for non-breaking hyphens in Microsoft Word, and I have found the way to do it at this blog entry at Allen Wyatt’s Word Tips: Ctrl+Shift+- (or Ctrl+_).
The non-breaking hyphen is used to keep a hyphenated phrase together across a line break. So, for example, the phrase “non-breaking” when occurring at the end of a line would not do this:
non-
breaking
nyctomachia 