I don’t think I have the time to really make a proper list. This question is an essay waiting to happen. Sooooooo, I’ll go top 3 with brief reasons for now.
1: Mara Jade (Skywaker)…duh. This is an easy one, because who would not want to see Mara come to life? She is a gigantic figure in the EU, basically being there and part of the reason, if you ask me, the EU was so successful in the beginning. We were happy to see our old friends, but then here is Mara injected into the mix right away, and she was electrifying with her story and background as the Emperor’s Hand. She instantly made it true that the EU was capable of creating new characters to play alongside the classic favorites.
2: Jacen and Jaina Solo. Again, an easy one. The story of the EU can easily be characterized as their story. We watched them both grow up into their eventual pivotal roles in the over all story of the EU. They grown and chance in magnificent ways to their final forms, that it would be a joy to watch that journey, despite knowing how it ends.
3: I’m going broad with this one, because I feel there are too many to just pick one: The New Jedi Order. The EU spawned an entire cast of new Jedi for us to enjoy and get to know, while legitimizing some old favorites like Kyle Katarn. One of my favorite scenes of all time in the EU is in Apocalypse where Luke is having a council meeting with all his Jedi Masters…and they are having a mock duel in the process! That was so much fun to read. Seeing all of them interact in at the height of the Abaloth crisis in that fashion….that was good story telling.