Strictly speaking, there are 10 countries on the physical continent of North America:
Canada
United States
Mexico
Guatemala
Honduras
Nicaragua
Belize
Costa Rica
El Salvador
Panama
"Central America" is a region, not a continent. If you're counting "North America" as a cultural region and not a geographical definition, then there are only two (Canada and United States).
Geopolitically, there are several island nations that are considered North American; this list would include The Bahamas, Cuba, Jamaica, and several Caribbean micronations. I am not familiar where the break between "North American" caribbean island nations and "South American" caribbean island nations occurs (for example, Trinidad and Tobago is generally considered South American, but what about Barbados? Could be either).
Greenland, Bermuda, and other territories could also be included in an extended list but it's important to note that they are not countries--they are dependent territories of another (non-North American) nation.
Finally:
Djazz: I think you must have slept through your geography class--you shouldn't brag too much on your "college graduate" status given the answer you provided. If you're going to include Mexico as a North American country, you also need to include the rest of Central America.
Chief: Your answer is terribly misleading as only the first 2 items in your list (US and Canada) are countries. The rest are dependent territories.
Hope this is what you are looking for, and hope this helps!
