Is any data safe?

Today another major retailer announced their customer files were compromised. This company had clearly implemented some security that kept hackers from getting too much information. Passwords were hashed and credit card numbers were kept on a separate server, which does signal that the company designed with security in mind. Nevertheless, personal information was compromised.
Is there anyway to keep information safe if it’s accessible from the internet? Some of my uber-security conscious friends would say no. I am beginning to believe them.