I'm a big fan of travelers checks. American Express even makes a "travelers check card" now, which looks like a debit card. Has the benefit of travelers checks (if lost, can be replaced easily) but the money is all loaded onto one card instead of having you get many paper travelers checks.
My thought is: with a debit card, if it gets lost or stolen, you're out of luck. With travelers checks or a travelers check card, you have some recourse. Many people use only debit/ATM cards these days, but they do have some limitations and potential problems.
Also, using travelers checks helps me keep track of what I'm spending. I like to allot a certain amount of money per day for food and souvenirs -- but using travelers checks, I know that if I'm coming close to my daily allotment, I need to cut back. With debit cards, it's easy to lose track of what you're spending.