Is the internet safe ?

In the last decade, the services offered on internet have increase at a drastic rate. Just to mention a few services that are available online, we can now pay our bills online and buy everything a person could possibly need. To have access to those services, you must give personal and private information. Is it safe to give our social assurance number, credit card number, email, phone number, email? We are giving every bit of information to someone how could possibly ruin our lives by copying our identity. How can we be sure that the information is in good hands?
I usually trust government sites and bank sites, simply because I would imagine that they have good security and a control system. I now realized that hackers are really good at what they do. A good hacker could be able to access that information even on a government site. It is a race between the hackers and the updating of their security and control systems.

What would the government do if a hacker would enter and copy their information? What would be the impact? These are questions that I do not know the answers to but hopefully the government has the answers.