Hyperion only in the eleventh place? What is wrong with people?
And how on Earth, 'The Thrawn Trilogy' didn't get enough votes to get into the voting stage
? I thought that we had some Star Wars fans here. Shame to you all!
I love the Star Wars films, but I've never read a single SW book...
Fix. That.
No idea where to start though... a lot of the books sound pretty awful to be honest. 
Haven't read them. My recommendation:
1) The Thrawn Trilogy - Absolutely brilliant, with the events of it happening 3-5 years after Return of the Jedi. Easily, the best Star Wars novels and IMO a must-read regardless of what happens with them. I doubt that the new movies will be near as good as them.
2) Darth Plagueis - a novel which gives the backstory of Plagueis, but also Palpatine. Fantastic novel and a must read for any Star Wars fan.
3) Movie novelizations - the prequel books are better. Revenge of the Sith is brilliant, while the other 2 prequels are quite good. The novelizations of old movies are skippable considering that there is no new info there.
4) Darth Bane trilogy - easy to read. It happens a thousand years before the movie events, and it tells the story of the Sith Lord who made the Rule of Two. It also explains a bit about Ruusan Reformation (why the Jedi aren't politicians and why the Republic doesn't have an army)
5) Revan - if you are into Old Republic stuff (have played KOTOR/TOR) then this is a must read. There another few books in Old Republic era. But if you haven't played the games, then skip it.
6) Kenobi - it tells the first 6 months of Kenobi after he goes into exile. Not much new info, but I love Obi-Wan
7) Labyrinth of Evil - it happens in the end of the Clone Wars. You'll learn how General Grievous got Palpatine.

Tarkin - from James Luceno. It is alright, though not as good as Darth Plagueis book.
Thrawn trilogy, Plagueis, Revenge of the Sith novelization and Darth Bane trilogy are the best in this list.
The novelization of the new movie is shit, though better than the novelization of the original movie. That sucked!