The following are countries that do not have or ceased using it's own national currency due to reasons one way or the other, such as hyperinflation, manufacturing costs (small population) or economy stability advantages etc.
British pound (since 760)
South Georgia and the South Sandwich Islands, British Antarctic Territory (?), Tristan da Cunha.
US dollar (since 1786)
Ecuador, East Timor, El Salvador, Marshall Islands,
Micronesia, Palau, Turks and Caicos, British Virgin Islands, Puerto Rica, Zimbabwe.
Euro (since 1999)
Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece,
Ireland, Italy, Latvia, Luxembourg, Malta, the Netherlands, Portugal,
Slovakia, Slovenia, Spain, Andorra, Kosovo, Monaco, Montenegro, San Marino, Vatican City, Martinique, Mayotte, Reunion, French Guyana, Saint-Pierre-et-Miquelon Islands, Saint-Barthélemy, Guadeloupe, Madeira and the Azores, Canary Islands
Swiss francs (since 1850)
Australia (since 1966)
Kiribati, Nauru, Tuvalu, Christmas islands, Norfolk Islands, Cocos & Keeling Islands
New Zealand (since 1966)
Niue, Pitcairn Islands, Tokelau Islands, Cook Islands
East Caribbean dollar (created 1976)
Antigua and Barbuda, Dominica, Grenada, St.
Kitts and the Nevis, St. Lucia, and St. Vincent and the Grenadines.
Chinese yuan (since BC)
Danish krone (since 1875)
Faroe Islands (also used there alone with own currency at par)
South African rand (since 1961)
West African franc (since 1945)
Faso, Ivory Coast, Guinea-Bissau, Mali, Niger, Senegal, and Togo
African franc (since 1945)
Cameroon, Central African Republic, Chad,
Republic of the Congo, Equatorial Guinea, and Gabon
Note: The Central and West African francs are interchangeable at par in all it's territories.
Note: this page is still under construction as more research is needed to get all the info up to date.