I've never had a debit card. Every time I've opened a bank account, I've asked for a plain ATM card with no Visa or MasterCard logo instead. It's safer because there's a mandatory PIN and an enforced daily withdrawal limit.
"Visa, accepted everywhere," I always thought, "Yeah, and everywhere Visa is accepted so is MasterCard." Apparently, that is not the case.
Just FYI, if you're traveling to a developing nation, make sure that your ATM/debit card will work to extract cash from your account.