If as an American you start investing outside the US, the red tape has only just begun. I'd caution you against it until you've met with a tax lawyer. You owe taxes on dividends outside the U.S., but what if the foreign investment doesn't pay out their dividends? You have to calculate a dividend you didn't actually receive, and pay on that. At least, that's what I understood before I gave up on the idea.
Speaking of which, if your bank accounts outside the U.S. ever add up to $10,000 you have to start filing "FBAR". While they would probably be lenient to a first time violator, if you fail to file FBAR knowingly they can penalize you for 50% of the account value or $100,000 (unfortunately I think it's whichever is larger...).