If coming from the US, get a CapitalOne 360 Checking account (formerly INGDirect).
With the debit card you can make ATM withdrawals with ZERO fees levied on the US side. (The only possible fees are by the local ATM/bank.)
In my experience this is easily the most cost-effective way to bring your money around. The exchange rate is always at least as good as anything you can get from a money-changer. Example: While in Macau recently, I got a rate of 1 USD = 7.967 MOP. Even in a very competitive market for money-changers, one rate I saw was 7.872, or about 1.2% worse.
Hence, even in countries where the ATMs usually levy some fee on international cards---e.g. Thailand ATMs usually charge 180 THB (or 5.64 USD)---you will still save money by withdrawing from the ATM, rather than changing your money with a money-changer.
Needless to say, ATM withdrawals have the additional advantage of being safer and more convenient than lugging around a lot of cash or travellers' cheques.
With this account, you can also instantly check online how much USD exactly was deducted for your X amount of local currency withdrawal. So if you'd like, you can even test the waters by withdrawing a small amount first and see what the rate is. If it is worse than the local money-changer rate (which I have never experienced), then you can go with the money-changers.
P.S. The only inconvenience with the CapitalOne card is that you can only withdraw a maximum of US$500 worth of money per day.
P.P.S. There are probably still other fee-free cards for international ATM withdrawals, but this is the one that I know of. I'd be very interested in learning about other similar cards.