Han Solo, if you include all his EU backstory. Boba Fett if you take his backstory prior to the Prequal Trilogy, when it was changed to the lame clone thing. Chewie, Corran Horn, Dash Rendar, Mara Jade, there's a lot of characters I like.

In terms of a strictly EU character, than Kyle Katarn, the star of the Dark Forces and Jedi Knight games is my all-time favourite, because he's one of the few who has mastered both sides of the force and can use both without falling to the dark side (that often).

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