There are several different "none of these" options that have been implemented. Many of them are only implemented in private elections (as distinct from public elections; e.g. elections within unions or student elections or internal elections in political parties).
One is "Re-Open Nominations" (aka RON). If elected, then the nominations have to be re-opened and then the election re-run. Sometimes, those nominated the first time are ineligible to be nominated again.
A second possible result is to create a casual vacancy (as if the elected person had died in office), which is then filled by the normal mechanism for filling a vacancy. If that normal mechanism is a by-election (US: special election) then this is effectively the same as RON. But it may not be; for instance US Senators are elected, but vacancies are filled with appointment by the state's governor.
A third possible result is that the office will sit unfilled for one term and its powers cannot be exercised for that term. This is more common with elections to committees or parliaments - the parliament is just one member short for a few years.