Although I didn't enjoy her introduction, Ed (Edward Wong Hau Pepelu Tivrusky IV, as she has named herself because ... Ed) quickly won me over with her weirdness and eccentric personality, which, according to the commentary on the DVD, was based upon Yoko Kanno, the brilliant composer of the series' soundtrack (this makes me really want to find her wherever she is in Japan and watch her). She's a bit feral, at one point attacking a shackled bounty and biting him like a cat, and seems to be more interested in non-humans and other fellow oddball geniuses, such as her close relationship with Ein and with Chessmaster Hex from "Bohemian Rhapsody."
Ed is also very similar to Ein, in that her past is only kind of touched upon, which like I said yesterday is cool with me. I like being left in the dark in some areas, particularly ones that aren't pertinent to the plot but add layers to the characters. We know that Ed lived in an orphanage on Earth, that she is exceptionally gifted with technology, and is an outcast by personal choice. And that's all we really need to know. Truly. Little bits and pieces are revealed later in the series, but her role on the Bebop and relationships with her crewmates is what is important.
I didn't get as tearful as others did apparently when she left the ship, but it did definitely give me the idea that the show was ending. I know that Ed seemed a little extraneous in a lot of ways - her being a bounty hunter wasn't really in her character, but she cared about the others on the team, so her helping out was her way of showing that - but when she went in search of her father back on Earth, it was a little bittersweet, especially considering what happens in the episodes following her departure.
I feel like a lot of anime tried to recapture Ed but didn't really get what made her so different and loveable. It wasn't just that she was unconventional; she was secure in who she was and operated out of care and concern for others, even those who were just as inscrutable as she was (see above: Chessmaster Hex). Most of all, she was essential. Even in the early episodes before she basically forced the Bebop to take her in, the show didn't feel complete; Ed was that missing piece of the crazy puzzle that made the series work so well. I guess Yoko Kanno is what made all of this possible.