The most helpful posts in this thread tend to be from folks who have actually tried head-to-head comparisons of different cards to see what the results are. It has been repeatedly shown that what the banks officially say the fees are isn't always the case AND that with recent volatility in the foreign currency markets, it's often a crapshoot what kind of rate you'll get, since rates can easily vary by more than 1% simply by virtue of a transaction being processed a day or two later.
A close friend recently visited Thailand and agreed to do several head-to-head comparisons of ATM and credit cards that are generally recommended in this thread and
on the wiki. On the credit card side, he compared cards from
CapitalOne (a basic cash back rewards Visa),
Schwab (the new Invest First Visa) and
TD Bank (an older account obtained from Commerce Bank before TD took it over). On the ATM side, he compared ATM cards on his
Citigold Checking,
Schwab High Yield Investor Checking and
TD Bank NY Yes Checking accounts.
The methodology: When he would visit an ATM, he would withdraw money from more than one account one right after another (all from the same ATM just minutes apart). And when he checked out of hotels, he would ask the clerk to divide the bill between different credit cards. In the end, he did five 3-way and two 2-way ATM shootouts, and one 3-way and one 2-way credit card shootout. All of this was done over a bit more than a week in Chiang Mai and Bangkok.
The results: From what we can tell, all of these cards are indeed fee free, but there were some subtle variations among them and our favorite for both credit and ATM usage is Schwab.
On the ATM side, for example, TD Bank and Schwab came out almost identically at every withdrawal, and Citi lagged behind every time. This is not to say that Citi charges a fee, as the difference was varied from about 0.4% to 0.8% (if they were adding a 1% fee, we would expect to see the rates occasionally vary by more than 1%), but Citi/Mastercard appeared to be using slightly less favorable rates than Schwab/Visa or TD/Visa. Note that this does not mean you will have the same results in other countries--or even during other weeks--as it is entirely possible that Visa was simply getting better THB/USD exchange rates than MC that week. But it does suggest that TD and Schwab may on average be slightly better options.
On the credit card side, we have less data, but again Schwab and TD proved the winners by a slight edge. The three-way shootout used a small amount (just 100THB), and CapOne came in at $2.86, while TD and Schwab each came in at $2.85, so it's hard to tell if the penny difference is significant or just a rounding issue. The two-way shootout, however, used a larger amount (1400THB) and yielded a more significant difference: $39.85 for Schwab vs. $40.09 for CapOne (a 0.6% spread). Like Citi, it doesn't appear that CapOne is adding any fee, and the difference may simply have to do with when the transaction was processed (although both cards are Visa cards and were swiped within minutes of each other, the transaction posted a couple days earlier to my friend's CapOne account than to his Schwab account, and exchange rates changed during the interim).
Based on this test, Schwab seems to offer the best credit and ATM card options as a primary card for most US travelers. Schwab's 2% cash back on credit card purchases, and their unlimited ATM fee rebates (if you encounter ATM fees overseas--they still aren't nearly as common overseas as they are in the US) make both their credit and checking products excellent--perhaps unbeatable--options for international travelers. TD comes very close, but since TD bank accounts aren't available nationwide, and new TD credit cards supposedly carry a 3% fee (my friend's account appears to have been grandfathered at the 0% Commerce rate following the Commerce/TD merger), TD won't work for nearly as many people reading this forum as Schwab does.
All of that said, Citibank (if you qualify for Citigold, Private Bank or other high-end accounts where they waive fees) and CapOne (ignoring their atrocious customer service) remain excellent options for overseas use as well.
edited to add: See also
Part II of this shootout, with data from a trip to Mexico in December 2009.