European law affords individuals the "Right To Be Forgotten" online. Essentially, if content on the internet would damage your life should it be seen by those near you, your legal right is to demand that the powers that be and everybody with the power to help come together to scrub the unsightly content from the face of the web. Naturally, the very nature of the internet imposes restrictions on this sort of thing. After all, if you do something embarrassing in the background of a news broadcast and it winds up on YouTube, Vimeo and tons of other video sites, there isn't much that can be done to stop it from spreading. Aside from the natural limitations of the medium, however, there are also certain restrictions of a more arbitrary fashion, depending on the authority in question.
For Google, requests under the law come in the form of people asking to have a URL hidden from their search engine's eyes, essentially ensuring that somebody would need to obtain the URL or navigate to the content from somewhere else in order to see it. There are a great number of cases where such requests are granted, such as high school fight videos that could ruin a college grad's job prospects or images of a very private and less than savory nature being put on the internet by somebody who was entrusted with them. For the most part, these sorts of requests fall under the rules that Google has set for honoring requests in agreement with European officials. A great number of requests, however, do not comply with Google's rules and are thus denied.
Google's number one purpose for denying a "Right To Be Forgotten" request is that the content at hand pertains to an individual's work life, not their personal life. Small businesses getting negative reviews online, former employees whose reasons for getting fired are broadcast, and people caught in conflict of interest situations with the evidence put online are some examples of the sort of requests that Google may end up denying under this reason. As the request pertains to a person's professional life, there are no personal details, which is what the law protects. The next most popular reason, believe it or not, is that the person making the request actually created and uploaded the content themselves. People who undergo a genesis of image often make requests of this nature, as do those who may have, at one point, confessed to unsavory activity online, only to find themselves regretting the admission. The denial of these requests is a stark reminder that just about anybody could be one misguided message board post away from being seriously humiliated or even rendered nigh-unemployable. The third most common denial reason, strangely, is that somebody is requesting to have information about another person hidden.
Also among those who find their requests lawfully denied by Google are, in order, those who request to hide a page that does not show a name, people asking Google to hide their own social media profile, people whose antics are "topical and in the public's interest", as well as the "relevant" variant of these people, followed by requesters who point to content that does not refer to a real person. Public personalities such as celebrities, tech rock stars, and politicians will also find that Google can and will lawfully deny their request, leaving their adoring or abhorring public able to easily find out the truth. The second from the bottom is people actually requesting to have government records hidden from view, which would likely not be on Google in the first place if they were not in public records, likely police booking records, for example. Of course, there is an "other" category for all of the oddball denials, nestled safely at the bottom of the list. The number of reasons within that "other" category could be nearly infinite, of course. Whatever the reason may be, the fact that some are denied is a reassurance that these requests are all investigated on a case by case basis, meaning Google is doing their part, at least in the EU, to respect peoples' right to privacy without compromising free speech.