For Asimov star with "I, Robot". Then I'd move on to the Elijah Bailey detective novels ("Caves of Steel", "Naked Sun", "Robots of Dawn"). I hear the Foundation series is also good but haven't read it.
I'm a big fan of Anne McCaffrey's world of Pern, which starts with "Dragonflight", "Dragonquest", and "The White Dragon".
I also like Terry Brooks and his watered-down Tolkienish post-apocalyptic earth in the Shannara series (Sword, Elfstones, Wishsong, and then more) and his Magic Kingdom of Landover series.
Terry Goodkind's "Wizard's First Rule" and "Stone of Tears" are excellent, but then his series bogs town for me.