If people think things are private online they are fooling themselves. You can delete your cookies and browsing history, but yet still you will get pop ups and then ads suggesting things for you to buy. It seems risky putting your information on the Internet, because it seems it gets snatched up somehow.
Private browsing might ensure that you do not have a record on your computer of what you do online, but it is nonetheless not private. If security and spy agencies can spy on individuals, I am pretty sure that they have the capability to spy on people who think that they are browsing privately. It'll require a great degree of technological sophistication to erase one's footprint in a way that it is untraceable to others.
The real question is the definition of "private." Online browsing is no really private since the server logs of the POE (point of entry) to the Internet are still able to narrow a port to a specific user and recover the IP addresses that user visited. So in a strict sense it's not private, but the reality is to 99.999% of the world it is private.
As we become more aware of the security risks posed by the use of the Internet, we come up with new ways to try and solve the problem, such as so-called 'incognito' browsing in the popular Chrome web browser and other such tools. But the fact is, for a true hacker, there are almost always ways around these measures.