Most mesmerizing, Tom Hardy in Bronson, singular protagonist, wow, just wow. Most redeems the entire movie, Alan Rickman in Robin Hood: Prince of Thieves, manages camp and fearsome, fabulous nemesis. Always worth a shout out re great characters, Eric Bogosian in Talk Radio, another singular protagonist, intense, complex, unpredictable.

I have some suggestions, and they are listed in order of who I would like to see
featured on the site most to least: Michael Coreleone (Protagonist), Tony Soprano (Protagonist), Gordon Gekko (Mentor/Nemesis),
Don Draper (Protagonist), Scarface (1983) (Protagonist), Tyler Durden (Mentor/Trickster/Nemesis, Jack Torrance (The Shining) (Protagonist/Nemesis),
Howard Beale (Network) (Protagonist) and Maria Elena (Vicki Christina Barcelona)(Attractor/Trickster).
I know you may not be able to feature them as ordered but all of these characters
pique my interest.

Two characters that instantly come to mind from movies that I continue to watch year after year: Travis Bickle from "Taxi Driver" and Edward Scissorhands from well...they named the movie after him.

TRAVIS BICKLE: I would argue that Travis is the protagonist and antagonist in "Taxi Driver" because he seems to continually create his own obstacles when trying to get what he wants= "All my life needed was a sense of someplace to go. I don't believe that one should devote his life to morbid self-attention." - Travis

I think what also makes Travis one of the most interesting characters in cinema is that he is not 100% sympathetic like the "hero formula" in the average movie.

Robert De Niro makes us earn every inch of sympathy we end up having for this guy. And like any person in real life, Travis has the potential for good and bad behavior, depending on the given circumstances.

EDWARD SCISSORHANDS: This misunderstood fairy tale protagonist faces an incredible antagonist: the entire suburban town that either prejudges him or tries to exploit him.

Edward's child-like innocence and good intensions make him instantly sympathetic. His goal is also relatable - he just wants to date Winona Ryder like the rest of us did as kids in 1990.

I love how Tim Burton made Edward's gothic appearance contrast completely with the "Easter Egg Pastel-colored" world he strived to assimilate into. Like Pinocchio mixed with Freddy Krueger.

Both of these guys are also VISUALLY unforgettable. Travis: you immediately think Mohawk and green army jacket.
Edward: literally white face, black leather and metal fingers.

The moral of the story: a great protagonist doesn't always have to be likable - just interesting.

@ question.authority - Jack Torrance from "The Shining" is an awesome choice. Jack is another great complex "Protagonist/Antagonist" character.

Geoffrey Rush as The Marquis de Sade in QUILLS. My take is that The Marquis is the Mentor character and Joaquin Phoenix's Abbe du Coulmier is the protagonist... and you know it's going to be interesting when the Marquis is your Mentor!

Mel Gibson as Mad Max, particularly in THE ROAD WARRIOR. I love this protagonist because he's so emotionally armored, he's a freaking Brinks truck. This protagonist also follows the template of the hero from the typical Western. He comes from outside civilization to save it from predatory forces, but, once his job is done, he must return to the wasteland, as he is an uncivilizing force himself and can not fit into "town" life. Thus, things that make him the only one capable of saving "decent" folk - his strength, resilience, and willing to go do what it takes to win or go down swinging - are a barrier between him and the people he saves in the end. Fascinating stuff!

Protagonist - Sheriff Ed Tom Bell in NO COUNTRY FOR OLD MEN. A strong character but one of the most ineffective protagonists in film history. He fails at everything he attempts - except his journey to greater acceptance of a chaotic world.

Nemesis - Tracy Flick in ELECTION. How can you not love a nemesis who offers an opponent a cupcake at their lowest moment?

Attractor - girl in the white T-bird in AMERICAN GRAFFITI. Only onscreen for 30 seconds or so IIRC, but that's enough to fuel Curt's journey.

Mentor - Don Corleone in THE GODFATHER. Hadn't really thought about this character in terms of his function before, and it's a little startling to find he's in the same category as Obi-Wan Kenobi!

Trickster - the Thing in THE THING. Really a nemesis, but obviously has a foot (and a claw, and a tentacle) in the trickster camp as well.

Hi Scott, I'd suggest Col. Vincent Kane - one of the more unusual protagonists for sure! The Ninth Configuration remains a classic and Stacy Keach's performance is as haunting today as it was then.

Vanessa Lutz in Freeway. For reasons I explain here:

http://postmortemdepression.blogspot.com/2010/06/off-topic-ode-to-vanessa-lutz.html

Oh - if you ever want to do a pair of great characters:

H.I. McDunnough (Protagonist) and Edwina "Ed" McDunnough (Antagonist) from Raising Arizona. I believe it's the baby, little Nathan Arizona, who's the Attractor.

Protagonist: Rupert Pupkin -- The King of Comedy

One of the great movie creations. A character who wouldn't really work in a short story or a novel. He fits best on the screen, where we see him in spite of the fact that we know he wants to be seen and *should* therefore turn away. We recoil from him because we know he's real, but we can't help but feel for him because deep down, he's us.

http://www.youtube.com/watch?v=8oLdPSjfnMQ

Nemesis: Sheldrake -- The Apartment

Like many great villains, Sheldrake dangles two opposing moralities in front of the protagonist (C.C. Baxter) and asks him to choose. One the one hand is success and fortune. On the other, the woman of his dreams. In many movies this would be a perfunctory choice but Billy Wilder's ingenious structure makes the success Sheldrake offers not some kind of random, Scrooge McDuck kind of fortune, but the very thing Baxter has been chasing the entire film. It's all the effort Baxter has expended pursuing this goal which makes his decision to discard it one of the most romantic acts in the movies.

Attractor: War/Glory -- Patton

He lusts for it with all his might and soul. He pursues it like Pepe Le Pew persues, well... a black cat to rape. The film is at pains to show that Patton is in love with his destiny, which is why his wife, to whom he was married to 35 years or so in real life, is to my knowledge never mentioned.

http://www.youtube.com/watch?v=wMQeJsV4pf4

Mentor: Cancer -- Ikiru

Imminent death is the only thing that can snap the star of Akira Kurosawa's Ikiru out of his bureaucratic stupor. It sends him on his journey of self discovery and eventual grace in one of the wisest and most moving films ever made.

http://www.youtube.com/watch?v=_mLrLHDdXHI&feature=related

Trickster: All the best ones I can think of I'd rather not post, for fear someone out there hadn't seen the film and would be surprised by it.

Thanks, folks. A good list. I'll definitely work up some Great Character posts with some of these. Feel free to add more.

Col. Hans Landa from Inglourious Basterds

[...] there’s no story to The Last Waltz, but there are narrative archetypes stirring in the stew. Their Mentors, above, have taken them as far as they can. Joni Mitchell, [...]