Law can mandate that search data remains entirely private: never stored, profiled or sold
As much as it would be nice, it will never happen. It won't happen because the governments of the world WANT that search history. How many times have you read an article about someone being accused or even charged with something although there was a lack of physical evidence implicating them because their search history revealed something that could be spun to be navarious?
By the way, if you ever search "how to kill someone" or "how to dispose of a body" (say, as trying to get ideas for plot points in a short story you are writing) you had better hope that nobody around you ever dies, because they WILL try to use that search against you.