This one's been going around. They're in alphabetical order by character name. Look out for spoilers for the characters' fate.
Adriana La Cerva (The Sopranos) - She was the one character on the show who was able to remain uncorrupted by organized crime, right up to her exit. That was a huge turning point for the show and it's been missing something ever since.
Angel (Buffy/Angel) - On Buffy he was one of the best villains the show ever had, but other than that rather uninteresting. However, the longer his own show went on, the more complex he got, culminating in a finale where he makes a series of incredible sacrifices to try and save the world. It's heartbreaking stuff. And this occurs in the same season in which he turns into a puppet. That's range.
Anya (Buffy) - She started out as a fantastic comedy character, drawing attention to the absurdities of human behavior. However, that naivete was wrenching in "The Body," and her ultimate choice to fight in Buffy's final battle is full of such mixed feelings. Is she embracing her human side, or has she been so messed up by recent events she doesn't care if she dies? Regardless, the final shot of Xander looking for her dead body is the most haunting moment of the series finale. Plus, her solo episode, 'Selfless' perfectly encompasses the way that Buffy can mix really broad comedy with heartbreaking tragedy.
Brenda Chenowith (Six Feet Under) - One of my favorite moments in the series, when Brenda yells at Nate not throw his engagement ring at her because "it's so cliche, I'll fucking barf" encompasses everything great and flawed about her character. This is someone who's so worried about not being normal and boring she's trying to preserve her originality rather than engage in the emotion of that moment. Her growth in the final season was astonishing and I love the way things ended up for her. Rachel Griffiths' work here is one of the all time great performances.
Christopher Moltisanti (The Sopranos) - Christopher is an endlessly frustrating character, someone who has dreams outside of the mob world, but can never quite make it. It's painful to watch him continutally fail, never more so than in the series' best episode, 'D-Girl,' in which he comes so close to getting out, but winds up retreating back into the family at the end.
Dale Cooper (Twin Peaks) - From his very first scene, Cooper is a fully formed personality, totally unique. I love his blend of rationality and mysticism, never better realized than in the early episodes, where his quest to save Tibet and throwing of rocks at bottles provides great entertainment. His mad run through the black lodge is another character highlight, pushing the best TV episode ever forward on the back of his personal tragedy.
David Brent (The Office) - He's absolutely hilarious throughout the series, but what makes Brent special is the few moments of humanity, his crying when he's fired and his sadness throughout the Christmas special. The "Fuck off" to Chris Finch is such a satisfying moment of character growth.
Faye Valentine (Cowboy Bebop) - When she joins the crew, they start to become a family and it's that uneasy family connection that makes for most of the emotionally powerful moments in the show. My three favorite Faye moments are the older her watching her younger self cheering for her on video and realizing that her life is nothing like what she expected. Then, the heartbreaking moment where she runs to find her childhood home and finds nothing but an empty lot, and finally, her tearful request to Spike not to go after Vicious, one of the saddest moments in all of TV.
Gob Bluth (Arrested Development) - The funniest character on a show stocked with hilarious characters. His ridiculous level of sleziness, the "Final Countdown" dance, Franklin. Some bizarre and great comedy.
Jack Bauer (24) - The Jack Bauer Power Hour is called that for a reason. At first it seemed implausible that Jack could do so much, but it's become a conceit of the show and now you just accept that this guy can do anything. I love the way that an entire military division could fail, but you send in Bauer and you get the job done. There's such an underlying sadness to the character, as he is forced to sacrifice all personal connection to get his job done. The last hour of the show has to end with Jack's death.
Jet Black (Cowboy Bebop) - The gruff on the surface, but big hearted father figure to the Bebop crew, the thing I love about Jet is the way that he never says how much he cares about them, but we know that he'd do anything for his friends. His two best moments are when he rescues Faye in "Jupiter Jazz," and his quiet request to Spike not to go after Vicious. He loves them so much, but he can't save Spike.
Lindsay Weir (Freaks and Geeks) - She's someone who's looking for a higher purpose for life, but finds nothing in her suburban environment to match her lofty ambitions. I love her search for personal identity as she moves uneasily between social worlds.
Lorelai Gilmore (Gilmore Girls) - Another woman in search of her place, though this one's a lot older. Lorelai is one of the funniest characters on TV, but it's her tragic side that appeals to me. She desperately wants something more from life, but feels like she'll never be able to find it. I loved her sad journey through the sixth season, particularly the painfully awkward speech at Lane's wedding. But, it's not all bad, her enthusiasm and quirks are always entertaining, she's someone you'd want to hang out with.
Fox Mulder (The X-Files) - His total devotion to finding the truth was the fuel behind the entire series, but what made Mulder so endearing was his quick wit and ability to move from deeply serious stuff to really goofy quipping. The character took on a life of his own and made the series what it was. Just look at the post Mulder episodes to see how crucial he was.
Nate Fisher (Six Feet Under) - Nate is someone who always wanted more, he was looking for a higher purpose in life, a more fulfilling relationship, a more meaningful existence. This quest is what propelled him forward, but it's also what doomed all his relationships. Nate's story is a tragedy, but you can still respect him because he never settled. The other Fishers may have been built for ordinary life, but that existence was toxic to Nate. He was the soul of the show and my favorite TV character of all time.
Nick Andopolis (Freaks and Geeks) - Yet another character in search of something more than his everyday life, Nick was undermined by his lack of initiative and work ethic. His work in the final episode is brilliant, the character still clinging to the hope of a relationship with Lindsay throws himself into an apocalyptic disco dancing contest. I don't see good things in his future.
Dana Scully (The X-Files) - I don't think it was either Mulder or Scully who was crucial to The X-Files, it was the combo. They had such perfect chemistry, it could enliven even the stupidest monster of the week episode. However, when they did get the emotional mythology stuff, Scully went to many intense emotional places, always remaining relatable. She went through so much awful stuff, but remained strong through it all. Their relationship was the show by the end, and it was great.
Sharon Valeri (Battlestar Galactica) - The ultimate questioning of purpose, Sharon had to deal with the revelation that she wasn't actually human, while simultaneously another Sharon was dealing with the fact that she was a cylon, but could have human feelings. I love the line between artifical and human life and this character is like a TV version of Roy Batty. Her appearances kept the middle chunk of season two watchable.
Spike (Buffy the Vampire Slayer/Angel) - Here's a character who totally owned every scene he's in. It's no coincidence that the show started to get good when he first appeared, and Angel had its best season during the time he was on. Spike was such a charismatic character that he made everyone he interacted with more interesting. Buffy was the most interesting during his season six trysts with Spike and Angel was at his best when the two of them worked together. I love the way Spike tries to project this really cool image, but is a sappy romantic at heart. He's full of endless complexities and there's no character who's more interesting to watch.
Spike (Cowboy Bebop - Another complex Spike, he's the cool image of Bebop, totally above emotion and feeling. At first this is his attraction, but as time goes by, we see that it's his greatest flaw. The end of Cowboy Bebop, and Spike's role in it, is totally frustrating, but it's the only way he could have went out. Rarely do you see such a tragic character depicted on TV, someone who just can't move beyond his past.
The Smoking Man (The X-Files) - Whenever I saw William B. Davis in the opening credits, I knew that we were in for a good episode. Davis owned every scene he was in, and is the ultimate representative of conspiracy in fiction. As time went on, he became more complex, and his tragic nature was never better expressed than in 'Musings of a Cigarette Smoking Man,' or particularly in 'En Ami,' where we saw a man whose whole life has been squandered consigning himself to death. He's a very compex antagonist and despite Carter's best efforts, the character never lost his cool.
Tim Canterbury (The Office) - The ultimate everyman, he hates his job, but can't get it together to move beyond it. His facial expressions are priceless, look at Hat FM, or any scene with him and Gareth. His quiet "She said no by the way" in the second season finale is one of the saddest moments in the show, and his joy when Dawn returns is the best moment in the whole series. It's difficult to make a really ordinary character and not make him boring, but they pull it off with Tim.
Tony Soprano (The Sopranos) - The most complex TV character of all time? Maybe, he's certainly one of the most interesting. Tony is at a slight remove from the mob world, aware of his moral transgressions, but endlessly justifying them, blaming them on his mother or claiming that every white collar businessman is doing the same thing. He's a distinctly early 21st century guy, caught between alpha male tradition and the need to be more sensitive today. He's never been more interesting than post coma when his new moral code forces him to break out of traditional patterns.
Wesley Wyndham Price (Angel) - Wesley's journey is what makes the character so interesting. He starts out as a hopelessly inept guy not suited for the real world and ends up a hardened warrior so emotionally numb he has to die. And, that journey is totally organic, there's no one moment of change, it just happens as time passes and then you look back and realize how far he's gone.
Willow Rosenberg (Buffy) - Much the same, Willow has a huge evolution over the course of the series and is almost always more interesting than Buffy herself. I love Willow and Oz and I love Willow and Tara. Hannigan can do comedy and drama with equal skill and I hope that she does some serious work soon and doesn't just get typecast in a sitcom nitch.