The Google Blog has an article titled Updating our “right to be forgotten” Transparency Report and what it's about is how some people desire to have all information about themselves removed from Google's index. 

You know if you go to Facebook or Blogger, or Twitter, you can remove all of your posts and pictures. But that's not something that people usually think you can do on sites you don't own like Google. Google indexes lots of web pages and maintains cached copies of web pages. For a person who might have information out there on the web that doesn't cast them in a favorable light, having information about them removed from Google's database might be a good option. 

I think that many people are going to learn that publishing information about themselves on social media is a mistake. They may not realize it at the moment. But what seems like a good idea now might not seem like a good idea later.