There are 15 FIDE members that are not members of the United Nations. What stands out about this list is that 7 of the 15 are British or British Dependencies. Here is the list:
7 British and British dependencies: England, Scotland, Wales, Bermuda, Jersey, Guernsey and British Virgin Islands
2 Dutch Aruba and Netherlands Antilles
2 USA Puerto Rico and US Virgin Islands
2 Chinese Hong Kong and Macau
1 Denmark Faroe Islands
1 Israeli-occupied Palestine
Name Population Owner Source
Aruba		70,441		Dutch	http://www.cia.gov/cia/publications/factbook/geos/aa.html 
Bermuda		63,960		UK	http://www.cia.gov/cia/publications/factbook/geos/bd.html 
British Virgin Islands	21,272		UK	http://www.cia.gov/cia/publications/factbook/geos/vi.html 
England 
Faroe Islands		46,011		Denmark	http://www.cia.gov/cia/publications/factbook/geos/fo.html 
Guernsey		64,587	British crown dependency	http://www.cia.gov/cia/publications/factbook/geos/gk.html 
Hong Kong	7,303,334			China	http://www.cia.gov/cia/publications/factbook/geos/hk.html 
Jersey		89,775	British crown dependency	http://www.cia.gov/cia/publications/factbook/geos/je.html 
Macau				461,833	China	http://www.cia.gov/cia/publications/factbook/geos/mc.html 
Netherlands Antilles		214,258		Dutch	http://www.cia.gov/cia/publications/factbook/geos/nt.html 
Palestine			3,300,000			http://www.odci.gov/cia/publications/factbook/geos/we.html 
Puerto Rico		3,957,988		USA	http://www.cia.gov/cia/publications/factbook/geos/rq.html 
Scotland 
US Virgin Islands		123,498		USA	http://www.cia.gov/cia/publications/factbook/geos/vq.html 
Wales
Most are islands which are far away from the mainland. Exceptions are Hong Kong and Macau, which were British and Portuguese until recently when they became part of China, and the Channel Islands of Jersey and Guernsey, which are in the English Channel and are closer to France than to England.
By far the smallest is the British Virgin Islands. Their chess teams have always included players who do not live there but who live in the United States of America instead. Their leader is one Captain Hook.
The US Virgin Islands used to do this too, but for the past 20 years have had a rule that players on the chess team must actually live there. The US Virgin Islands has a history of sending chess teams containing players who do not play chess at all and who just learned the rules of the game for the purpose of getting a free all expenses paid vacation in the country which is hosting the World Chess Olympiad.
There are 45 UN Members that are NOT in FIDE:
Benin, Bhutan, Burkina Faso, Cambodia, Cameroon, Cape Verde, Central African Republic, Chad, Comoros, Congo, North Korea, Democratic Republic of the Congo, Dominica, Equatorial Guinea, Eritrea, Gabon, Grenada, Guinea, Guinea-Bissau, Kiribati, Laos, Lesotho, Liberia, Maldives, Marshall Islands, Micronesia, Nauru, Niger, Oman, Palau, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Samoa, Sao Tome and Principe, Saudi Arabia, Sierra Leone, Solomon Islands, Swaziland, Timor-Leste, Togo, Tonga, Tuvalu, Vanuatu.
http://www.un.org/Overview/unmember.html
Thanks again to John Fernandez for compiling the above list.
Sam Sloan