In my wallet:
1 VISA with no foreign transaction fees (happens to be a UA Mileage Plus card, but spouse got that card primarily so wouldn't lose a lot of accumulated miles with UA)
1 debit card

In passport security pouch:
1 Mastercard with high credit limit to get me out of a jam if necessary (just happens to be a Mastercard; never had problems using VISA overseas)

I once arrived overseas to find that my debit card didn't work in airport ATM and had to take out a cash advance with credit card. Luckily I had internet access and transferred cash from bank account to credit card that day so wouldn't accumulate ridiculous interest. I suppose it would have been helpful to have another debit card, but having only had the problem once, I don't bother.