Which bank offers the most favorable check/debit card for the worldwide traveler? I ask because my current check card nails me for a 1% foreign transaction fee every time I use it overseas. I prefer to use Amex but it's not accepted everywhere.

Coincidentally, I've been doing a little reseach on that very subject. As far as I've been able to find out 1% is actually relatively good.
My B of A debit card charges a flat $5 for each international cash advance, regardless of the amount. My usually trusty visa card charges $10 or 3%, which ever is higher, on top of their cash advance interest rate, and other fees, and this is even if I have a credit balance! In other words, they charge me hefty fees just to access my own money!
I have found a local bank that charges just a dollar per international cash advance. As usual, these things are often negotiable if you have the time and inclination to deal with banks.
Often regional banks who are trying to grow will penalize you least. But remember, these are fees that any bank can change at any time, without notification.

Like Spiral says, it'll vary but best you can do is just have a wander sround the CBD of errrr.. Antartica during your lunch break and see who has the warmest welcome in out of the cold hard world banking can be.
If by chance you're going pass through UK and can open a Nationwide account they're supposed to be pretty good for no withdrawal fees.

If you're in Western Europe, BofA is part of an alliance with some banks (Deutsche Bank, BNP Paribas? and some others) and won't charge $5 for withdrawing from them.

Otherwise, I've heard credit unions have low overseas withdrawal fees.

Totally go for the credit unions. But each individual bank has its own system. I traveled with my debit/credit card from the California credit union and the only thing i was ever charged was whatever the ATM fee was...usually a dollar or two, but was never charged through my bank.

It may not be your BANK, but the little Visa/MC logo that lets you use the card that's causing you the 1% fee. I reaaaaally looked into this a couple years ago, things may have changed since then, but what I learned was:

Visa and MasterCard charge 1% fee for foreign purchases. If that's all you're getting charged, you're actually lucky, as some banks actually charge a fee on TOP of that. Even for "credit" cards, as opposed to debit cards, the issuing bank (i.e. MBNA, Chase, Capitol One) may charge another fee on top of.

Last I checked, Capitol One didn't charge and extra fee, nor did MBNA.

As for debit banks, like someone said above, Bank of America whacks you with a $5 fee for ATM withdrawals, BUT if you take out a couple hundred bucks (US) at a time, it almost balances the 1% for making purchases with the card instead of cash. That's what I usually do (Taking out $500 to totally balance the fee can be a bit risky, but it depends how much cash you're comfortable with)

For UK people

Nationwide.

100%

Get a flex account, very safe, no ATM fees,accepted everywhere (cirrus/maestro).

Then just take a good VISA/MASTER card and that's all you need. Maybe a spare US$200.

You might try HSBC. They're a huge international bank with ATMS and branches in tons of countries. I opened an account with them in the US, but as long as I use an HSBC (whatever country I'm in) ATM, I won't be charged any fees for withdrawls. You get a free Mastercard Debit/ATM card with their checking accounts.

Plus, they have a great online savings account offering higher interest rates than ING Direct.

Veto HSBC

When you use another bank the charges are high and they also have a very unfriendly customer services dept.

Just to clarify Nationwide flex account does not charge for ANY ATM withdrawl, ANYWHERE in the world.