So, I've shared this before. I've not read any of the newer books, so all the below fall under the Legends banner:
Darth Bane Trilogy: Path of Destruction - Rule of Two - Dynasty of Evil
Properly introducing the, ah, much loved character of Darth Bane to the EU (he appeared in an earlier comic, but the book supersedes that) it gives a rich, detailed look into the philosophy of the old Sith Order, and the Rule of Two of which Bane is the first master. The first two books, in particular, are among my favourite SW books; They're really well written, and the author seems to take a certain amount of glee in mercilessly killing off named characters, innocent characters, Jedi, Sith... There's a lot of killing in these books
Darth PlagueisA fantastic read, detailing the rise of Sidious under his master from rage-filled schoolboy to Supreme Chancellor... Lots of wonderfully gruesome scenes, lots of sly shots at the Jedi, but also doesn't stint from portraying the Sith as evil; You
understand them, but you don't
sympathise with them...
Episode IEpisode IIRepublic Commando series: Hard Contact - Triple Zero - True Colors - Order 66 (There's a 5th book, Imperial Commando: 501st, but it was intended to set up a new series which has now been cancelled.)
This looks at the lives of a squad of four ARC clone troopers. All four are the survivors of squads who otherwise died on Geonosis, and the series looks at how they start to bond, how they work with the Jedi, how they work with other squads and how they relate to their training officers - some better than others. The series is divisive among those who've read it; The author clearly has little regard for the Jedi overall, and the way they acted during the Clone Wars and their treatment of the clones under their command in particular. That said, the action is good, the characters are diverse and the stories are well written.
Episode IIIStar Wars: Revenge Of The Sith - I admit that I've not read it, but the novellisation of the film is reputed to be excellent, expanding on character motivations in the right places.
KenobiDeals with Obi-Wan's arrival on Tatooine, and how he sets about acclimatising himself to life there. Obi-Wan is realistically scarred and beaten by his experiences in EpIII, and the mystery that forms the core of the book is a good one.
Dark Lord - Rise of Darth VaderSet immediately after ROTS, this tells how Vader adapts to life as a Sith apprentice and how some of the surviving Jedi cope with the change in their lives
Coruscant Nights trilogy: Jedi Twilight - Street of Shadows - Patterns of Force
The last Jedi on Coruscant begins to adapt to life without the Order, and form the connections that will help the Rebel Alliance on the Imperial homeworld. This feeds into a 4th novel,
The Last Jedi, which is also worth a read, but thematically and in story terms is separate from the trilogy.
Han Solo Trilogy: Paradise Snare - Hutt Gambit - Rebel Dawn
Some of Han's backstory (A lot of it remains a mystery, deliberately so) as Han matures over the decade leading up to his meeting with Luke and Obi-Wan in the Mos Eisley cantina. It's not too much of a spoiler to say that the central romance is deeply affecting - even if, of course, it can't end happily.
Episode IVScoundrelsBest described as Solo's Eleven
Episode VTales Of The Bounty HuntersAnthology book set during/around Empire Strikes Back and follows the bounty hunters hired by Vader to track down the Millennium Falcon. A really enjoyable read, as unlike the other two books in the series (
Tales from the Mos Eisley Cantina and
Tales from Jabba's Palace) the stories range far and wide with their characters without too much overlap. Not to be confused with the
Bounty Hunter Wars trilogy, which open with sub-par covers and go downhill from there)
Episode VIX-Wing - Rogue Squadron - Wedge's Gamble - Krytos Trap - Bacta War
These first four books of the series detail how the New Republic takes Coruscant and holds it, seen from the view of the Republic's premier starfighter squadron. Michael Stackpole, the author of the books, is one of the best writers of action around, and that lends itself very well to the fantastic dogfight and other action scenes that come up frequently in the books.
Thrawn Trilogy: Heir to the Empire - Dark Force Rising - The Last Command
The first books published, post-ROTJ, in 1991 I believe. That's something to bear in mind as the books have been written over the course of 20+ years, and while Lucasfilm gave editorial oversight, the books introduced superweapons, darksiders and other wild concepts that just didn't end up mattering in the long run. It must have been difficult to write the books knowing that people would want something recognisably Star Wars, while at the same time being something new as well. Still, for me at least, a lot of the 'early' books released in the 1990s just don't stack up to the later releases.
Anyway, these books are set five years after the films, it details the ongoing conflict between the New Republic and Empire, and introduces the legendary Imperial Grand Admiral Thrawn. The trilogy's not a bad place to start, as the writer (Timothy Zahn) is one of the finest writers in the EU.
X-Wing: Wraith Squadron - Iron Fist - Solo Command
A different squadron and a different writer for this trilogy, which deals with the campaign waged against a rogue Imperial warlord. This series, more than most in the books, is in turn both hilarious and emotional. The second book, Iron Fist, is one of the finest standalone books in the EU.
I, JediA standalone counterpart to the
Jedi Academy trilogy, which consensus varies on. This is one of the first books to take an in-depth look at the training of a Jedi. Beyond that, it's also a storming adventure in its own right. It's the only first person EU book, starring one of the pilots from the Rogue Squadron series of books.
X-Wing: Starfighters of Adumar
Same author as the Wraith Squadron books, this is a straight-up hilarious book.
Hand of Thrawn Duology: Specter of the Past - Visions of the Future
Winding down the New Republic/Empire war, this brings back Timothy Zahn to tie up the plot strands ahead of the next major series of books.
After this, the books shift into several long series which continue the general storyline of the main movie characters, series punctuated by standalone books and shorter series (such as the Coruscant Nights trilogy).
The continuation series are as follows:
New Jedi Order - 19 books - Way, way too many books; They didn't try this again. About half are worth reading, I'd say, and about as many advance the plot... they're not always the same books.
Traitor is the standout book in the series.
Dark Nest - 3 books - Haven't read these.
Legacy of the Force - 9 books - Grim, grim, grim. I read these once and got rid of them. They do bring about a major change in the EU, but 9 books can pretty much be summed up effectively by the Wookiepedia plot review.
Fate of the Jedi - 9 books - Lighter than the previous series, while at the same time introducing a quasi-demonic entity who helps stir up a galactic vendetta against the Jedi... But where the previous series seemed bogged down under its own weight, this one pretty well moves along at a decent clip, and by introducing a lost tribe of Sith into the series, offers some nice counterpointing of the Jedi and Sith ways.
There are some good books out there I've not included in the list, either because I've not read them or they're not really necessary to follow the overall story. Where I've underlined books, they are
especially recommended as being integral to the overall EU, or otherwise as being particularly good writing. However, it's all just a recommendation. Read what you want, and have fun doing it