America, 8: Summer, 1904 in St. Louis, 1932 and 1984 in Los Angeles, 1996 in Atlanta; Winter, 1932 and 1980 in Lake Placid, New York; 1960 in Squaw Valley, California; and 2002 in Salt Lake City, Utah. Denver was supposed to host the 1976 Winter Olympics, but backed out due to cost overruns.
France, 5: Summer, Paris in 1900 and 1924; Winter, Chamonix in 1924, Grenoble in 1968, Albertville in 1992.
Japan, 4: Summer, Tokyo in 1964, and scheduled to host again in 2020; Winter, Sapporo in 1972, Nagano in 1998. Tokyo was supposed to host in 1940, but those games were canceled due to World War II. It's just as well, since Japan was one of the aggressors in that war.
Britain, 3: Summer, London in 1908, 1948 and 2012. London was supposed to host in 1944, but those games were pushed back to 1948 due to World War II.
Canada, 3: Summer, Montreal in 1976; Winter, Calgary in 1988, Vancouver in 2010.
Italy, 3: Summer, Rome in 1960; Winter, Cortina d'Ampezzo in 1956, Turin in 2006.
Germany, 3: Summer, Berlin in 1936, Munich in 1972; Winter, Garmisch-Partenkirchen in 1936. Berlin was supposed to host in 1916, but those games were canceled due to World War I. It's just as well, since Germany was the main aggressor in that war.
Russia, 2: Summer, Moscow in 1980; Winter, Sochi in 2014. As Bob Costas pointed out last night, because of the 1980 boycott, this is the first Olympics in Russia in which America has participated. And we got a nice hand from the Russian crowd. I wonder what Putin thought of that.
Greece, 2: Summer, Athens in 1896 and 2004. There was a 1906 Olympics in Athens that sometimes gets counted, because it gets credit for restoring the "Olympic Movement" after the travesties of 1900 and 1904, but the IOC does not officially count it.
Australia, 2: Summer, Melbourne in 1956, Sydney in 2000.
Norway, 2: Winter, Oslo in 1952, Lillehammer in 1994.
Austria, 2: Winter, Innsbruck in 1964 and 1976.
Switzerland, 2: Winter, St. Moritz in 1928 and 1948.
Korea, 2: Summer, Seoul in 1988; Winter, Pyeongchang is scheduled to host in 2018.
China, 1: Summer, Beijing in 2008.
Spain, 1: Summer, Barcelona in 1992.
Yugoslavia, 1: Winter, Sarajevo in 1984 (now in Bosnia).
Mexico, 1: Summer, Mexico City in 1968.
Finland, 1: Summer, Helsinki in 1952. Oddly, despite Finland's reputation as a cold-weather nation, it has never hosted the Winter Olympics.
Netherlands, 1: Summer, Amsterdam in 1928.
Belgium, 1: Summer, Antwerp in 1920.
Sweden, 1: Summer, Stockholm in 1912. Due to Australia's animal quarantine laws, Stockholm also hosted the equestrian events in 1956.
Brazil, 1: Scheduled to host the Summer Olympics in 2016.
North America 12
South America 1 (in 2016)
Africa, so far, never
In an English-speaking country: 16
German: 7 (both Swiss Olympics were held in the German part of the country)
French: 5 (6, if you count Quebec)
Dutch: 2 (Antwerp is on the Dutch side of Belgium)
Nations that, at the time, were...
Democracies: 45 (presuming Brazil stays democratic through 2016, South Korea does so through 2018, and Japan does through 2020)
Dictatorships: 8: Germany, both of 1936's Games; Mexico, 1968, they had elections but who was kidding who; Russia, 1980 and 2014, I mean Russia has elections, but who's kidding who; Yugoslavia 1984, China 2008