The Foundation Trilogy by Isaac Asimov--probably my favourite sci-fi series out there.
The basic plot is that a guy named Hari Seldon (if I remember correctly) is a psychohistorian, basically a guy who has studied people's behaviours to the point that he can basically predict the future.
He predicts a massive war that tears the peacefull alliance apart and creates a plan for a select group to follow to shorten the years of chaos by a great amount.
It really is a great trilogy, and I don't want to say any more and give away anything important. It's filled with plot twists, cool technology, and just a very enjoyable read.
Ah, completely 100% agree with Clinterus. The Foundation series is briliantly writtent. Asimov at its best.
Only, one addition. It is not an average "predict the future" story. The story in the series stretches over thousands of years. Only other series comparable to it in its scales is Dune series. Asimov smartly uses predicting the future plot as a basis for introducing other numerious and much more interesting plot lines.
Also, it's not really a trilogy. The main sequence has five books (seven if you include the prequels, and even more if you include books by authors that are not Asimov). And the shift in tone is placed not between the third and fourth book, but rather in the middle of the second one (all the stuff with the Mule, for example, is very indicative of the style of 4th and 5th book). The fifth book and the prequels also serve to create a narrative bridge between the Foundation universe and the Robot universe - in a way, making a single continuity.
One thing to remember - those books are not modern, and do contain certain anachronisms of their time as far as the view on technology and social structures go. They are great books, make no mistake - classics in the sci-fi genre and well deserved of that descriptor - but they are not the cutting edge of sci-fi nor the cutting edge of inquisitive/deep-reaching literature.