The Consumerist reports
on a problem one of its readers had when he was hit by fraudulent debit card charges from his Bank of America checking account. According to the reader's story, Bank of America first reimbursed him for the fraudulent charges, but later decided to reverse those reimbursements. Due to his low balance, he was also hit by overdraft charges.
Of course there may be more to the story than what is mentioned, but it does show the problems that can occur with a debit card. Even Bank of America's highly-advertised $0 Liability Guarantee may not be enough.