Arthur Frommer recently let you know about the United Plus Explorer card, which waives the foreign transaction fee the way the famous Capital One suite of cards does. That card (in which, I stress, Frommer's has no financial interest) is described in his blog post.
But that's for a credit card. What about cards linked to savings accounts, which let you draw money you actually have rather than spend money you borrow?
For that, there's Charles Schwab — in which, again, Frommer's does not have an interest beyond telling you about it as a valuable financial travel tool.
An account with Schwab requires no minimum balance, grants free checking, and most usefully for travelers, doesn't charge you a transaction fee if you use an ATM anywhere. If the institution running the ATM levies a fee of its own (and many do), it reimburses your account for it.
If you should use it as a Visa card instead of an ATM card and draw directly from your account, it also waives that annoying 1% to 3% foreign transaction fee. To Schwab, earning your business and receiving your savings is incentive enough for it to swallow both of those fees. Despite that savings, Schwab doesn't get cheap on customer service: That's 24 hours a day.
You'll find details about that account, the High Yield Investor Checking, at this link.