The implications of the internet and search engines specifically are generally understood. You can just Google anything generally considered to be a fact and you can find it instantly. For those of us who have been through the public school system, or really any school system, this is good but also kind of scary.
If memorization now means almost nothing, what was school for?
This is a larger question than I have time to answer here, but let me apply it to one traditional school subject - foreign languages.
Learning foreign languages in school is a tedious affair. You sit down and memorize an endless list of words and learn a few grammar rules on top so that you don't sound like an idiot. The emphasis in my own experience, and from what I can gather is the norm for learning a foreign language, is on pure memorization. Throwing vocabulary at the students until they just absorb more and more.
The best way to really learn a language is a sink or swim approach. You have to just throw yourself into it with minimal support and just struggle through it. I became much better at Spanish by living in Chile for 5 months than by learning in a classroom for 5 years. Teachers of foreign languages know this is the best method. Their vocabulary spewing approach is an unfortunate necessity. Not everybody gets the chance to live in the country of the language they study.
But the vocab approach may not be the case for long. The internet and Google especially make things like facts easily accessible at no marginal cost. Because of this language teaching will change in 2 ways.
It will eliminate the necessity to work on vocabulary based activities. It will improve the speed and efficiency with which these activities are performed by students. Instead of spending countless hours on memorizing vocabulary, all you have to do is look these words up and you'll know them instantly.
The elimination of vocabulary building activities (which account for an ungodly percentage of the time students spend in foreign language classes) will allow for students to focus on the really important parts of a language: grammar and mechanics. When I say grammar, in English we might think of the uses of "their, there, and they're" but grammar is much more useful and far less semantic than that. What I mean is that students will be able to focus on how sentences are formed, how do people actually speak? Once you know how things are actually formed, everything else can be filled in quickly with online dictionaries. In my experience speaking Spanish with native speakers, a grammatical or syntax error is much harder to correct than a vocabulary based error.
Cut the vocab. Learn HOW to say things, not WHAT to say. (Not to be taken out of the context of learning a foreign language.)