In Star Wars Insider UK #77, Daniel Wallace recommends a number of essential EU must-reads/must-plays/must-sees recommending various EU media for you, some of which I think have done more harm than good to the constinuity, and others which I think are right on. I'd like to offer my additional recommendations in this entry (some of which have also proven unhealthy to the continuity, I might add).

The original list
Wallace's original list is as follows:

Novels:
Must read: Thrawn Trilogy (Heir to the Empire, Dark Force Rising, The Last Command)
Don't overlook: New Jedi Order series

Comicbooks:
Must read: Dark Empire
Don't overlook: Star Wars Legacy

Reference works:
Must read: The New Essential Chronology
Don't overlook: Behind the Magic

Games:
Must play: Knights of the Old Republic
Don't overlook: Dark Forces II: Jedi Knight

Television:
Must see: Clone Wars, the microseries
Don't overlook: Star Wars: The Clone Wars

Expanding the Expanded Universe list
...And here are my recommendations:

Novels:
Must read: Splinter of the Mind's Eye - it's quite well written, and then it's a seminal EU-novel - it does contain a couple of things that are perhaps a bit incompatible with present-day canon, but that makes it an even more interesting read
Don't overlook: I, Jedi - stands out by being written in first person, and recounts, uiquely in the perspective of Corran Horn events known from other novels

Novellas:
Must read: The Dark Forces trilogy (Soldier for the Empire, Rebel Agent, Jedi Knight) - dynamic and action-packed canonical descriptions of many of the events of Dark Forces II: Jedi Knight, which also fills many of the gaps in the computer game.
Don't overlook: Side Trip - the first Zahn-Stackpole collaboration, which in itself makes it worth mentioning, this novella features a number of EU darling characters.

Short stories:
Must read: A Boy and his Monster: the Rancor Keeper's Tale - the heartbreaking story behind the crying rancor keeper in EP VI
Don't overlook: Charlene Newcomb's Alex Winger stories, which carved out a corner of the Star Wars continuity of their own

Comics
Must read: Star Wars Marvel comics stories featuring Shia Brie/Lumiya (Coffin in the Clouds, Hello, Bespin, Goodbye, Sundown, Shira's Story, Screams in the Void, The Mind Spider, Figurehead, No Zeltrons, Duel With a Dark Lady, Escape, First Strike, All Together Now) - firstly, they tie in with the Legacy of the Force series, secondly, a lot of them are simply darn good stories, especially Hello, Bespin, Goodbye, Screams in the Void, No Zeltrons, and Duel with a Dark Lady.
Don't overlook: Evasive Action - the story of a surviving pack of padawans, and I still think it should be released in TPB form! It features a number of popular characters.

Reference works:
Must read: any Star Wars Adventure Journal gaming article - probably not reference works as such, but nonetheless full of canon.
Don't overlook: Wookieepedia - not official, but full of info and growing every day.

Games:
Must play: Galactic Battlegrounds - loads of epic canonical battles and missions
Don't overlook: Shadows of the Empire - the video game aspect of the Shadows of the Empire multimedia project.

Television:
Must see: Star Wars Holiday Special - of course :-P
Don't overlook: The Ewoks movies - left a lot of retconning to be done

Honorable mentions
Novels: Shadows of the Empire
Novellas: Interlude at Darknell
Short stories: Tales from Mos Eisley Cantina collection, Tales from Jabba's Palace collection, Peter Schweighofer's Dirk Harkness stories,
Comics: Shadows of the Empire, Knights of the Old Republic (TOJ), Redemption, Knights of the Old Republic series,Betrayal, Darklighter,The Savage Heart, To the Last Man, 8 for Aduba-3, Droidworld, The Last Jedi, Death in the City of Bone, Outlander, Oh! Jawajawa, Perfect Evil 1 and 2, Rookies, Rogue Squadron.
Reference works: Galactic Phrasebook and Travel Guide, all New Essentials, StarWars.com database, Star Wars Encyclopedia (although arguably outdated now - but I've heard there's a new edition on the way)
Games: Mysteries of the Sith, Jedi Outcast, Jedi Academy, Force Commander, X-Wing Alliance (although I dislike the last couple of levels), Rebellion (only partially canonical).
Television: Droids, Ewoks (I wonder what they were on when they made that).

That was my list of Expanded Universe recommendations. You're invited to make your suggestions in the comments section.