D&D Alignment Matrix—in graphic form, generally accurate enough for most purposes. Although there are other schools and differential interpretations. 
Chaotic villains are entertaining. They’re often super hammy over the top personalities and a great source of surreal situations and comedy. I guess indulging in baser desires isn’t supposed to be as mature and sophisticated, but meh.
My favorite kind of villain is the knight templar trope, or I guess you could call it the anti-hero maybe. Basically someone who thinks they’re doing good and won’t let anyone stand in their way. Everyone is the good guy of their story, but this person usually has the same or similar goals to the protagonist yet go about it in an extreme, more self righteous way. I don’t know where that fits on the D&D spectrum. Usually interesting because they make the audience or even the heroes say, “crap, they got a point!”
Maybe I find them a little more terrifying than your normal 9-5 punch clock villains because they’re the true believers with big ideas. The kind of people who can really screw everything up. The religious fundamentalists. The general Rippers. The social warriors (wherever on the spectrum). The uber nationalists wanting to restore the nation’s glory. They know they have the solution and it’ll make everything better but everyone else is just too stupid/cowardly/corrupt to see it.
Magneto is a liar, a hypocrite, a criminal and a backstabber. He isn’t lawful anything.
A list of fine villains who aren’t D&D “lawful” is a very long one. Just from movies; The Joker, Hans Gruber, Keyser Soze, Anton Chigurh, Hannibal Lecter, Tommy Devito, Michael Myers, John Doe in Seven, Annie Wilkes, Alex, Dr. Szell…
None of those necessarily disqualify you from being Lawful Evil. Well, arguably they’re practically required for the “Evil” part. Even as a criminal, breaking someone else’s law in the course of trying to impose your own is still lawful. Conversely, a Lawful Good person wouldn’t feel constrained by the laws of a totalitarian evil regime they were trying to overthrow. You’re lawful because you believe in the necessity of a strict code of conduct and structure of hierarchy.
AFI created a top 50 list of movie villains. Here are their top 14, along with my guess at alignment.
- Dr. Hannibal Lecter, Silence of the Lambs, LE
- Norman Bates, Psycho, CE?
- Darth Vader, LE
- Wicked Witch of the West, NE?
- Nurse Ratched, One Flew Over the Cuckoo’s Nest, LE
- Mr. Potter, It’s a Wonderful Life, LE
- Alex Forrest, Fatal Attraction, ?
- Phyllis Dietrichson, Double Indemnity, NE?
- Regan MacNeil, The Exorcist, ?
- The Queen, Snow White and the Seven Dwarfs, NE?
- Michael Corleone, The Godfather Part II, LE
- Alex De Large, A Clockwork Orange, CE
- Hal 9000, 2001: A Space Odyssey, LE
- The Alien, Alien, NE
Corrections welcome.
So far: I have 43% LE, 29% NE, 14% CE and 14% ??.
It can go either way. The best examples I can think of off the top of my head are a couple of characters from Order of the Stick: Daimyo Kubota is (well, was) a corrupt noble who wanted nothing more than to increase his own personal power, and damn the costs, but who preferred to use existing social structures (which he’s near the top of) to do so. That’s pretty clearly evil ends, pursued through lawful means. By contrast, Redcloak, one of the main villains of the story, just wants his people, the goblins, to have a fair shake at life, with quality land they can call their own, and a civilized society… but he’s willing to risk the destruction of the world and all the souls within it to attain that. That’s lawful ends, pursued through evil means.
Another thing is that most people’s alignments are just part of their general make up. In the real world, most Americans would qualify as “lawful” in that they’d agree that a system of law is necessary for society. But very few would actually crusade or put themselves out to promote bringing law to the lawless, at best it’s a pretext to feel better about military campaigns (“We’re bring them democracy…”). Likewise, most people would generally agree with “good”: acts of charity, kindness, etc but few make it their driving goal, sacrificing deeply to feed and clothe the homeless or something.
But in games, alignment is an easy crutch for giving NPCs a personality so it tends to be magnified. It’s not enough to be a decent guy who respects society, you need to be Lawful Good.
Marvel’s best villain, Doctor Doom, is the law of his own nation. He is protected from repercussions when he is at his Latverian Embassy in New York, and even gets police* escorts. And he literally rules with an iron fist.
** not really police*
I give you the archetypal worst villain of the Lawful Evil category: Dr. Evil. Meticulous. Organized. Hierarchic. Fond of elaborate extortion schemes, a form of contractual evil. Also prone to the “unnecessarily slow dipping machine” kinds of machinations.
Forgive me if I find Dr. Evil less impressive than, say, Heath Ledger’s Joker.
When I think of Lawful Evil, my first though was Mr. Potter in It’s a Wonderful Life. I wonder if they had him hide away the $10 grand (which he found and didn’t steal) just to make him unambiguously evil.
In certain sectors of society, troll like him and Montgomery Burns are extolled as Job Creators.
My first thought of Lawful Evil was Order of the Stick’s General Tarquin. Of course, my first thought for Chaotic Evil wasn’t the Joker, but rather OoTS’s Xykon. I guess maybe I’ve read too much Order of the Stick. But I bet Xykon could beat the Joker in a fight.
Taken out of context, parts of the original AD&D alignment descriptions can sound a bit… political 
HAL 9000 is a computer and hence neither good nor evil. However, it must follow the rules of its programming since, well, it’s a computer. HAL is therefore Lawful Neutral.
Lecter is a psychotic who demonstrates no regard at all for social order. Lawful characters, by definition, attempt as best they can to act within the rules of their society, even if that involves changing those rules. Lecter has NO regard for the rules of society, no regard for whether he is perceived as breaking the law, and is often barely able to control his own animalistic impulses. He is chaotic evil, absolutely a slam dunk.
“Polite and educated” isn’t “lawful.”
Your example of Nurse Ratched is a much better example of LE.
Homicidal… but not evil?
I thought Lector was methodical enough to be LE.
New list
- Dr. Hannibal Lecter, Silence of the Lambs, [del]LE[/del] NE, with a case to be made for CE
- Norman Bates, Psycho, CE?
- Darth Vader, LE
- Wicked Witch of the West, [del]NE?[/del] CE: Have a fireball!
- Nurse Ratched, One Flew Over the Cuckoo’s Nest, LE
- Mr. Potter, It’s a Wonderful Life, LE
- Alex Forrest, Fatal Attraction, CE
- Phyllis Dietrichson, Double Indemnity, NE?
- Regan MacNeil, The Exorcist, CE?
- The Queen, Snow White and the Seven Dwarfs, NE?
- Michael Corleone, The Godfather Part II, LE
- Alex De Large, A Clockwork Orange, CE
- Hal 9000, 2001: A Space Odyssey, LE with a case to be made for LN
- The Alien, Alien, NE
My revised list has 5 LE, 4 NE and 5 CE. Comments and revisions always welcome. This version tends to falsify the OP.
How would you classify him, then? The guy was the king-in-all-but-name of his own mutant haven. If we have to call him Evil (I’ve personally always much more enjoyed him as a shades-of-grey character than the ‘straight villain’ characterization Grant Morrison adhered to), then Lawful makes the most sense, as I understand the term.
Though, I suppose it depends on how you define the categories (and brings up the obvious limitations of it). Under the TVTropes types, I suppose he could be a type 3 - megalomanic who thinks he’s the good guy. This kinda seems to be going under the ‘neutral evils are just everyone who doesn’t care about law/chaos’ though.
Anyways, I think Lawful Evil types are the easiest to make into likeable villains. Not necessarily the best (as others have noted, there are lots of great villains who defintely aren’t Lawful Evil) but they’re easy to like.
I don’t think I’d call the creature from Alien evil. Particularly in the first film, it’s essentially just a dangerous animal. It’s not killing the crew out of maliciousness, or cruelty, or to advance any agenda other than “eat and reproduce.” That would make it True Neutral, like other animals.
As for Magneto and other comic book villains, these are characters that have been written by dozens of different writers over the course of decades. Their characterization can fluctuate wildly because of this. Stan Lee’s Magneto is a different shade of evil than Chris Claremont’s Magneto, who a different shade of evil than Grant Morrison’s. If you take them all together, these inconsistencies are almost always going to shade the character towards Chaotic Evil, simply because the villain who said one thing in one comic, is now acting a different way in a different comic fifteen years later.
That being said, I think Magneto at his “best” is neutral evil. He does not generally revel in causing misery, but he’ll stop at nothing to secure the future of his people, even if that involves going back on his own word or betraying a trusted ally - so long as it’s all in furtherance of his cause.
And those paladins that mow down thousands of evil minions are supposed to be good?
I think the best example of Lawful Evil I’ve seen was a demon* in one of the Neverwinter Nights games. A man sold the demon his soul, and the demon is claiming his reward. However, the contract is void if the demon “forced the human” to perform certain actions.
You can debate with the demon and the client and eventually prove the demon had tricked/forced the human to do what he did and thus violated the contract, voiding his ownership over the soul. The demon is extremely mad, but most importantly, he backs off and goes home because he accepts that he is bound by the rules of his contract.
- Devil, actually, because by definition in D&D “demons” are chaotic and “devils” are lawful, but whatever.
I don’t recall the movie well enough (aside from “open the pod bay doors”) to remember what was up with HAL. If it was just responding to glitchy programming, it wouldn’t be “evil” any more than an automatic sentry gun is “evil” for shooting whatever trips its sensors.
On the Evil Computer track though, we have GLaDOS. On one hand, science is a “lawful” practice at its core, but then GLaDOS doesn’t exactly seem concerned with strict protocols in her experiments. She’s also cognizant that her subjects are performing unwillingly and berates them throughout when not actively trying to kill them. I’d say she’s more Neutral Evil – she’s selfishly motivated by a mixture of perverse science (torture) and, later, revenge.
I think most people have an appreciation for order and structure so you’re already halfway there in gaining their sympathies. Chaotic Evil characters like the Joker might be “cool” in the moment but few people would say “I like idea of what he’s trying to accomplish here”.