Unfortunately, Lucusfilms has said that the books of the expanded universe (EU for short), may non be canon any more. But that's not to say that there are some really good reads. I'll list some of my favorites:
Thrawn Trilogy (Heir to the Empire, Dark Force Rising, Last Command) by Timothy Zahn - This is arguably the gold standard of the EU. It was also the run the re-invigorated interest in the Star Wars universe.
X-Wing: Rogue Squadron (Rogue Squadron, Wedge's Gamble, Krytos Trap, Isard's Revenge, Starfighters of Adumar) by Michael Stackpole - These books are where the expanded universe, really gets expanded. There is very little focus on the Big 3 (Luke, Leia, Han). It is about Wedge rebuilding Rogue Squadron and introducing new/lesser know characters and species.
X-Wing: Wraith Squadron (Wraith Squadron, Iron Fist, Solo Command, Mercy Kill) by Aaron Allston - This series is my favorite. It is about a unit that Wedge puts together to act as both a starfighter squadron and commando unit. You really get into the characters, their back stories and their interactions. The late Aaron Allston does an amazing job. You may wish to avoid Mercy Kill. It takes place in a future scenario and you may have to be really invested in the previous books to enjoy.
Hand of Judgement (Allegiance, Choices of One) by Timothy Zahn - I just started getting into this series, and I really like it. It is heavy on the action and morality. It's about a squad of stormtroopers that go AWOL after failing to comply with an immoral order. This series is almost right after Star Wars: A New Hope. It includes 1 of Mara Jade's (very prominent character in the EU) 1st missions for the Emperor.
Dark Lord: The Rise of Darth Vader by James Luceno - This takes place immediately after Star Wars: Revenge of the Sith. Shows the new status of the galaxy, the hunting of the Jedi, and the inner workings of Anakin now that he is encased in the Darth Vader suit.
Those are my picks. I'm sure others will add their favorites.