Zhan's Thrawn trilogy is probably the only real classic of post-1990 EU. For me, it was the one series of novels that had the Star Wars feel, while also expanding on it. This guy got Star Wars. The characters behave as they should, while also being taken in new directions, the story seems like a logical extension of the films and is told in an interesting way, and there is a very human emotional core to the story. As a ten year old, I found it a bit boring in parts but I appreciate it a lot, lot more today.

Anchorhead, if you want to check out EU you have to start with the Thrawn trilogy. It created and defined the EU for a decade, and there's a reason why many people wished Lucas filmed these as the sequel trilogy. I don't want to oversell the books, because they have their flaws, but they are pretty darned good in my opinion. I would also pick up the graphic novel of Dark Empire. The earlier EU was always really good, probably because they could write unrestrained, they created the continuity that boxed in later writers, which is why now it is difficult to write captivating material. Lucas solved this with his Clon Wars cartoon by simply ignoring the EU, and in many cases contradicting it.