Protection of your trademark outside the U.S. is an important consideration if you are or will someday be involved in international trade. Generally, international trademark protection is available on a country-by-country basis. And in most countries, ownership is based on registration alone, not use as in the U.S.
Especially as the marketplace becomes more truly global, it's important to be aware that a U.S. registration does not afford protection in other countries. Since other countries give priority to those who file first, attention should be given to identifying the countries in which you expect to be doing any substantial business before you commit to a name. Some countries do afford some protection to "famous" trademarks, say McDONALD'S, where a usurper has filed for the same mark in that particular country. But such rights even for the most famous marks are clearly the exception and not the rule.