When things are put on the internet, it's almost impossible to completely get rid of them. That is why it is important for people to be careful about what they want others to see. They need to find a way to control what can be found about them. Most personal information is found from profiles on social networking sites like Facebook, LinkedIn, Flickr, etc. All of these sites have privacy settings that a user should look at very carefully to control who can see what content. You can make sure only friends can see what you put up, friends of friends, or specifically pick who you want to see. Maybe there are some things you only want a handful of people to know; depending on the site, you can make that happen.
People with common names are less likely to have information found about them. Chances are if you have a common name, there are multiple people who have a more significant footprint on the internet than you. It is almost like you have privacy in obscurity. They might be famous for whatever reason, or an important figure in a big organization or cause. If you have a unique name, you should pay attention to privacy settings much more as any information is a lot easier to find.
Obviously, all of this is depending on what you want people to know about you. If you want to remain an insignificant speck of dust on the internet, the easiest thing to do is avoid using your real name. Maybe use a nickname, but only something only your closest friends and family know. As a general rule, just don't put up any information on the internet you don't want people to know. All these social network sites have options for birthday, address, employer, phone numbers, etc. Don't fill those out. If there are photos, videos, or something you wrote that you might be ashamed of, don't put it on. Once it's out there, it's nearly impossible to get back, so better be safe than sorry.
