From the time of the issuance of the first postage stamp in 1840, hundreds of colonies, territories, etc., have issued legitimate stamps and gone out of existence.  Some of the more remarkable of them that exist today are noted here, only to provide an idea of the breadth of "unusual".

Campione d'Italia - a piece of Italy inside Switzerland near Lugano.
During World War II, the town was cut off from the rest of Italy and asked the Swiss for permission to issue stamps.  It received that authorization and the issued stamps were valid on local mail and mail to Switzerland.  For some unknown reason, the stamps remained valid until 1952 - for seven years after the war ended. 

SMOM - Sovereign Military Order of Malta.  A  sovereign "state" with no territory.  Headquartered in Rome, Italy, the entity issues stamps in Euro values (under agreement with the Italian post office).  That are valid only on letters to other countries with which the Order has concluded a bilateral postal convention.  It is not a member of the UPU.

United Nations.  An international organization that issues stamps at its post offices in Geneva, Switzerland, Vienna, Austria and New York City, USA, by virtue of international treaties (headquarters and bilateral postal agreements) with the host countries. 

The Palestinian Authority.

Mt. Athos / Agion Oros

Jersey, Guernsey & Isle of Man

Nagorno-Karabach