It's not only governments that want to take your money. It's also the banks. But you knew that already.
The main thing I look out for is fees. Less fees are more good. And when you are using your money overseas there are all sorts of fees banks like to charge you. So when I was planning my move overseas I paid close attention to these fees. I guess there are two main fees to look out for: international ATM fees, and a fee for exchanging currencies (sometimes both by the bank and Visa/Mastercard/whatever). Currency exchange fees are often charged at a percent of the exchanged amount. That can cut into your margins which is especially painful if you don't have much margin for error. And a three dollar ATM fee could be a couple meals here.
Luckily, there are a some large banks that do not charge these fees, such as Charles Schwab and Capital One. Here is a wiki with more information. Capital One seemed somehow more evil, so I went with Charles Schwab. I opened a Schwab Bank High Yield Investor Checking account with them. When you open this type of combined account there are no relevant account fees, minimums, or activity requirements. As for the international fees, they reimburse any ATM fees charged by other banks, including overseas, at the end of each month. They also cover the Visa currency exchange fee charged by Visa. They don't charge any other relevant fees. So basically that means I'm not loosing any money when I use my card overseas (or otherwise).
I was hoping for a bank that made things easy to manage and set up. Compared to the other online bank account I have (which has horrible international fees), I would say Schwab falls quite a bit short in this regard. But once you are set up it doesn't matter too much anymore. I also needed to notify Schwab of my travel plans (by phone) so that they wouldn't block any transactions made overseas. For some reason, when one receptionist at a hotel tried to use my card to add another night, it didn't work. However, I was able to immediately go and use the card online to book the room. Not sure what happened there. So far I haven't noticed any fees being charged. Actually, it's a bit weird because ATM fees are supposed to be reimbursed at the end of the month, but I haven't seen any ATM fees in my transactions or missing from my withdrawal amounts. At this point I'm pretty happy with them in terms of using the card overseas.
You'll notice I haven't linked to Schwab. I don't like promoting companies (including this one) and I have no interest with Schwab. I just thought I'd share what I'm doing in case it helps you.