I've been thinking about that very point myself and have written a novel coming out in April of next year, based on this very concept (note: I am *not* trying to plug the book, but it *is* what I'm doing). It takes place in 2082, 30 years after the (literally) overnight collapse of all technology worldwide. This occurs subsequent to the so-called Singularity, and is caused by the Intelligent Internet (or what they call the Intellinet in the book).
Generally, SF tends to fall in one of two perspectives when looking at what happens when AI becomes more intelligent than humans...what I call the "Terminator" outcome where the AI seeks to destroy humans, or the Asimov "I Robot" outcome where it becomes a benevolent parent/servant. But I pose a third option...that the AI pulls the plug on humanity, says sayonara and takes off for the stars.
Anyway, this scenario was also deeply inspired by Thomas Cahill's "How The Irish Saved Civilization" so I have an organization called the Archives (located on an isolated South Pacific island) that sends retrieval specialists throughout the world to locate and recover all the knowledge and technology remaining in the ashes, to prepare for an eventual renaissance. One of the key factors that Cahill points out, which enabled the Irish to preserve knowledge through the Dark Ages, was the fact that it was an island society, far removed from many of the cataclysms that swept over Europe. And the knowledge existed in obscurity for the most part.
So this is one scenario which I foresee for rebooting civilization
Although this first book is already written, I will definitely spend a lot of time on these boards combing through ideas for the two sequels!