This is a big step towards re-writing history. It begins with ignoring it, or by actively hiding it. I give it 1 year before we hear of attempts by politicians to cover embarrasing stories that are relevant information to the public, or before corporations hide unpleasant past events such as oil spills (corporations are people too, these days). True, search engines aren't the sole gateways to information, but nowadays people assume that if something isn't found on the first search results page it's probably not important.
It happens already actually - off line.
The whole "right to be forgotten" is an implementation of the fact that over time, whatever happened people naturally forget about, and getting at those records is hard enough that the effort usually isn't worthwhile.
The Internet, though, is an ever-expanding pile of information, that stuff you did 10 years ago will haunt you for the rest of your life. It's so valuable a resource that industries that traditionally would've just let things slide because they happened so long abo the evidence is sketchy now has access to all the information that most people have long forgotten.
The right to be forgotten doesn't remove content, it just means that the link between the content and the specific search gets broken. There can still be searches that bring up the content (e.g., "BP" may not bring up the oil spill, but "oil spill 2010" can bring it up).
I suppose a common example would be employers who google every prospective employees, only to see that 10, 20, 30+ years ago they did something "bad" and declining to interview because of it. (Generally most content is undated, so determining how long ago something happened can be quite difficult).
Of course, there are also people who google their dates, etc.
And even before this ruling, brand management companies knew how to bury content - just because you did something horrible 3 years ago, doesn't mean you have it have it sit as the 4th link on Google. With a bit of SEO and other techniques, you can bury those past events farther down the line (remembering 90% of the people stop at the first page, and barely any reach the 3rd or 4th page of results, so if you get it page 15, it's buried, or forgotten).