I don't really think there is a country count, but if you've visited and experienced more than a handful of the world's great cultures, then I'd say you're well on your way.

By "world's great cultures" I guess it's somewhat continental, but not exactly. For example:

Eastern Europe
Central and Western Europe
Southern Europe/Mediterranean Coast
North Europe
North American
Caribbean
Latin American/South American
China, Japan, Korea
Thailand, Vietnam, and other countries of southeast Asia
Hawaiian and other Polynesian-influenced locations
Australia/New Zealand
Middle Eastern/North African
Sub-Sahara African