[wakeneddreamer]

If you're talking about listed stocks and such, then the licensing caveat I mentioned, so only some firms will be willing to take you, especially since US tax and securities laws are particularly strict. Easiest is going through a US-based ETF or mutual fund that targets the world ex US or specific regions/countries. Otherwise several US brokers can give you access to foreign stock markets at varying costs. Either will also simplify your tax situation vs. using a non-US firm (foreign bank and investment accounts are a US tax reporting nightmare, even if you live overseas, and also the US has agreements with many countries to exchange tax information, so you'll still need to pay). Whatever you do don't invest in a non-US mutual fund, as the tax treatment is usually quite punitive.

Note correlation across stock markets is higher the last 10-15 years than it has been before then, so that reduces the diversification benefits.