Non breaking space / non breaking hyphen
Non breaking space
OS X: Option-Space
PadKeys: Alt Space (suggestion)
Non breaking divis "-"
OS X: Cmd-Shift-hyphen
As of version 2.1, opt-space now produces a non-breaking space. This is indicated by the non-breaking space symbol shown on the right side of the space bar when opt is active. Non-breaking hyphen is the first option in the key popup menu for the hyphen key.
Please note that not all iOS apps support these characters and may convert them into their regular equivalents. For example, the Mail app does this conversion. On the other hand, Nebulous Notes is an example of an app which preserves the non-breaking attributes.
Jon Lang commented
You know how you've got combining characters on the Options layout in blue? It would be nice if you could color-code the non-breaking characters as well, or indicate their non-breaking status in some other way.