For ATM withdrawals, there is BOFI (Bank of Internet). They offer a certain level of refunds of ATM fees (both foreign and domestic), no foreign exchange surcharge, and relatively high interest (around 3.5% for checking). The drawback: daily withdrawals are limited to $US 300, no matter how much money there is in the account. Still, BOFI is good enough for getting small cash while traveling without paying outlandish fees.
I use FirstIB (First Internet Bank of Indiana) and have been using that for 4 years living abroad since 2001. It's excellent. Recently they started charging 1% fee on international transactions, however I am unsure if this is the standard 1% fee that VISA charges, or their charge.
Note: When using your ATM card in Europe, the international bank (let's say Barclays in the UK) cannot charge you a fee. They can only charge a fee for domestic bankholders (such as HSBC, which in most cases they do not).
Hence any charge of an ATM international withdrawl (other than the 1% VISA fee) is strictly by your local bank. For example, Bank of America charges a flat $5 fee per International transaction. Hence, if you withdraw $100, and get charged $5, that 5% which is still better than cash exchange offices abroad.