I am pretty sure the only tax you are exempt from by living overseas (as I do) is Federal. I still have to pay for Social Security and Medicare. If it was up to me, I would not pay either of those two as I too believe I can do better on my own. By the way, its the first $78K you are excluded for (it was for tax year 2001) and will increase in the next years.
No, I am not an accountant, nor tax expert, but living overseas has made me learn this stuff