[Kobeck]

IMO, the countries that the USA has been involved with in a military manner since 1850s. Not invaded as much as at least trained with. Official baseball sponsored tours have not been terribly successful overseas, but when Americans, soldiers mostly, have long term contact and can teach baseball then it has proven to be popular, not always but a lot of times. So to answer the question I think the following:

Mexico, Cuba, Nicaragua, Argentina, Uruguay, Paraguay, Columbia, Canada, Japan, British controlled parts of China, Egypt, Haiti, Chile, Korean Penisula, Saoma, UK, Spain, Phillipines, Abyssinia (Ethopia), France, Germany, Italy, China proper, Tiawan, Domenican Republic, Soviet Union, Croatia, Turkey, Guatemala, Costa Rica, Honduras, Newfoundland, Bermuda, St. Lucia, Bahamas, Jamaica, Antigua, Trinidad, British Guiana, Dutch Guiana, Iceland, Austria, Greece, Israel, Egypt, Vietnam, Lebanon, pretty much the Caribbean, Vietnam, Thailand, Cambodia, Laos, Congo (Zaire), Cyprus, El Salvador, Lybia, Grenada, Chad, Bolivia, Saudi Arabia, Kuwait, Iraq, Peru, Liberia, Bosnia, Herzegovina, Somalia, Macedonia, Central African Republic, Albania, Kenya, Tanzania, East Timor, Serbia, Yemen, Afghanastain, Georgia, Djibouti, Eritrea, Pakistain, Uganda, Jordan, Mali and a bunch of the 'stans' in the Caucasus region. And Im sure Im missing some - lol