Sometimes I have a hard time picking a favorite character from a single book or show, let alone out of all of them.
G'Kar and Death are both very, very high on my list (though I enjoy Londo more than G'Kar; Londo's arc is far more tragic, I think. He makes mistakes, yes, but then he pays, and pay, and pays for them.) I think Death is my actual favorite literary character of all time, but he has the triple-whammy of being funny, earnest, and playing with conceptual/concrete dynamics. It's pretty much a rigged vote.
Gosh, this is hard! Okay, okay. Hmm. All right, this is going to out me as a nerd among nerds, but...
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Favorite TV Show Character: Vash the Stampede from "Trigun." I love me a Don Quixote, and I'm particularly fond of how long Vash manages to keep up his smokescreen of "harmless goofball," if it even is a smokescreen. (Another similar character - whose ultimate status as either genius or lunatic is never actually clarified - is the titular character of "The Irresponsible Captain Tyler," which is mostly also quite a lot of fun.) More to the point, I very much understand and empathize with Vash's constant conundrum. He wants the spider and the fly to live in peace, with neither dying, and the series as a whole reinforces the message that while such a world is impossible, striving for it is not in itself a bad thing. (The biggest weakness, in my opinion, is that they let Vash get away with a little TOO much success on the basis of his ludicrous abilities.)
Runner Up - Uncle Eiroh from "Avatar: The Last Airbender." Uncle Eiroh is a pimp. That is all. (Notice he's also a Secret Genius self-disguised as a lovable and mostly helpless goofball. This is probably not a coincidence.)
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Favorite Book/Story Character - Jack of Shadows from "Jack of Shadows" by Roger Zelazny. Zelazny is hands-down my favorite author (yes, even more favorite than Pratchett). Jack is a lot like Pratchett's Death, in some ways; looking for humanity without realizing it. He's considerably more opaque, however; one of the things I like best about Zelazny is how rarely he lets us into his characters' heads. I've read this book probably twenty or thirty times and I still couldn't say with absolute precision why Jack makes some of the decisions he does. I regard that as a strength.
Runner Up - Captain Vimes. If I can't have Death, I'll admit to also being fond of Pratchett's most obvious Mary-Sue despite the obvious Mary-Sue-ness of him. "Fifth Elephant" is one of my favorite Discworld books, period.