http://www.infoplease.com/spot/winter-olympics-2006countries.html 80 Two parts to this answer: 1) There are no 2006 Olympics. There are only Winter Olympics this year. 2) 80 or 81 countries, depending on whether you separate the two Koreas or not.
There are countries that in the Continent of North America that are in the Olympics, just as countries from the continents of South America, Europe, Asia and Australia are in the Olympics. North America is a Continent with many countries in it.