Hal 9000 said:
I'm reading the Thrawn trilogy right now, as everyone says this is the more important. I like it so far; he seems to understand the characters. Afterward...
The Dark Empire comic series. Because why not.
I suggest you limit yourself to the first Dark Empire and ignore the two sequels. The first, while not stellar, has its merits, but Dark Empire II and Empire's End are beyond pointless.
I, Jedi - I'll read this one in place of the Jedi Academy trilogy for efficiency.
That's the best idea I never had.
The Black Fleet Crisis trilogy
I wouldn't bother. While the first book was very interesting, the final two entries are complete letdowns.
The Corellian trilogy
The best non-Zahn/non-comics EU anyone could ever read, and that isn't hyperbole.
New Jedi Order - An abbreviated run of just five entries: Vector Prime, Star by Star, Traitor, Destiny's Way, and The Unifying Force
The EU officially jumped the shark with the NJO - don't waste your time reading this tripe.
I would appreciate suggestions of which are the essential reads of the Legacy of the Force and Fate of the Jedi serieses. They're recent enough that I haven't found a reliable description of which ones are the barebones essentials.
I doubt anyone here would recommend - or even bother to read - either of those two series.