The last time we got Travelers Checks was when we got married almost 8 years ago. Usually we take some cash and use our credit card for pretty much everything. Just using the ATM when we need more cash for small purchases/counter service meals. Then we pay off our credit card when we get home.
It helps that we have separate CC accounts so if there's a problem with one, we can use another. (Never happened, but you never know).
That being said, I have been on vacation before and our "network" went down and and I couldn't get cash out for about 6 hours.
Also, DH and I have separate bank accounts. We make sure there is money in both before we go on vacation. On our anniversary trip to AKL for some reason the ATM wouldn't take his card, but it would mine.
The last time we went, we were on a package, so our room & tickets were already paid for before we left.
Also, I always leave a credit card in the safe for good measure.