I find it really strange that so few people have commented on this - this has the potential for huge impacts on the quality of information available on the Internet!
As far as I can see, the court must be populated by judges that have zero clue how the Internet works. The particular case that provoked the decision: A Spanish man went bankrupt, and his house was auctioned off. This is part of the public record in Spain (in particular, it appears in newspaper articles) and Google - obviously - has indexed this public information and provides links to it.
The court does not say that the newspaper articles must be removed - in fact, they are specifically allowed to remain. The court says that Google may be told not to link to those pages, when given a search on this person's name.
So now individual people can tell search engines "I don't like that link, delete it"? Even though the information is publicly available and objectively, factually true? Does this make any sense?
How will this scale, when millions of people want to edit their lives in the Internet? How are these requests supposed to be checked? First, what is the definition of "inadequate, irrelevant or no longer relevant" information? Second, how do you determine whether the person making the request is the person affected (especially given the possibility of shared names)?
Finally, what effect will this have on search results? What you want to hide may be exactly what I really need to know! Why does this businessman think his previous bankruptcy is irrelevant - is that not precisely the kind of information that his potential customers and/or employers are legitimately interested in?
This decision demonstrates appalling technical ignorance on the part of the court, and has the potential to seriously screw up the concepts behind public search engines.