If you are a US citizen you must report your income no matter where you made it, unless you live abroad and qualify for an exemption (I believe the income has to be less than $86,000 and you can only set foot in the USA for no more than 10 days). That's after you've paid the local taxes. It's called double taxation and frankly, it is unfair and sucks. The US is one of the few countries that engages in this.
If a brokerage you are using has business in the USA or it is domiciled in a country that has tax treaties with the US, it will most likely report your tax info to the IRS.
If you go to some tax haven, you are taking chances because lately there's been a lot of crackdowns on tax havens both by the US and the EU countries that are tax revenue starved these days. Once there's an information sharing agreement, you are screwed.