Let's say that I want to portray that I've just done something evil. Well that would be your standard, "I've got a fish-hook in my eyebrow and I like it".
The best way to portray amused superiority or superior amusement, the arched eyebrow is a prime weapon in the expression arsenal for the Chess Master, Manipulative Bastard or (in possibly the most famous modern example, hence the trope name) The Spock. Often raised just as the heroes comprehend what the Evil Plan was all about. For instance, finding out that by foiling one objective they helped their enemy achieve a second, the planner will arched an eyebrow as if to say 'suckers!'.
This may accompany an Eye Take: the raised brows make room for the widened eyes. And as Expressive Mask shows, even glasses and masks don't get in the way of the eyebrow.
Like rolling one's tongue or performing Spock's other trademark, this is not a talent everyone has. With enough dedication and some practice in a mirror, however, would-be Chess Masters can usually develop the skill.
Combine this with Twinkle Smile, and you get the Dreamworks Face.
This is not to be confused with Alistair Darling's eyebrows which, while fascinating, are rarely raised. Also not to be confused with Michael Dukakis'seyebrow-forests◊.
Examples:
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Advertising
Dreamworks' promotional posters do this ALL. THE. TIME. Actually, this applies to a lot of animated companies. The difference, of course, is that Disney, for example, generally limits it to an in-film expression unless it practically defines the character (there's a reason why Buzz Lightyear wears it on his poster and Princess Ariel doesn't, even though they both do it within their films).
The Nostalgia Chick's review on the franchise talks about their habit of doing this in great detail.
Although there's an inverse image macro parodying the one linked above making the claim that the same could be said about Pixar. Make of that what you will.
A running joke in Mad World is of Zack trying, and failing, to copy Sephiroth's automatic eyebrow raise. Turns out to be a family trait - Vincent and Yazoo can do it too.
Expect Billy Zane to do this a lot if he's playing a villain, most notably in Titanic.
Hugo Weaving, especially in The Lord of the Rings. There is a reason Elrond is famous for his eyebrows.
Literature
Vetinari of Discworld fame often used the Fascinating Eyebrow along with a finishing blow in a verbal power struggle to make sure the opponent knows he's been defeated. (This is highlighted in Making Money, wherein Cosmo Lavish, one of the antagonists, actually practices raising one eyebrow in front of a mirror in an attempt to emulate the Patrician.)
What's worse, Cosmo couldn't actually raise his eyebrow on his own. He has to rely on a small mechanical device to raise his eyebrow for him.
There is a small asylum dedicated to people who think they are Vetinari. They have eyebrow-raising competitions.
The bread and butter of all female characters in The Wheel of Time by Robert Jordan.
Along with sniffing and (if they're Siuan Sanche) snorting. Oh, for heaven's sake...
The protagonist of Are You There God? It's Me, Margaret. can raise one eyebrow and does it occasionally to get adults to stop asking her questions. She doesn't know why it has that effect, but it does.
The Queen's Thief LOVES this trope. Not only is the main character a master of this art, so is his love interest.
Elizabeth Bennet of Pride and Prejudice has a fascinating eyebrow that has a tendency to rise when she comes across things she finds particularly ridiculous or wryly amusing. It's one of the many pride things going on.
In Chrome Circle by Mercedes Lackey and Larry Dixon, Tannim's mentor, a dragon currently wearing human form, arrived (magically) in response to a call for aid and "raised one long eyebrow at Tannim in a gesture that Tannim knew perfectly well had been copied after long study of Leonard Nimoy."
In The Mortal Instruments Clary is annoyed when Jace does this at her, because it is an ability she has always envied. She gets even more annoyed when Magnus Bane turns out to be able to do it too.
During Galaxy of Fear a rather absurd suggestion is made, and Hoole raises an eyebrow. Tash thinks that "it was as close as her stone-faced uncle would ever get to looking surprised."
Live-Action TV
Supernatural has the Trickster/archangel Gabriel do this a lot just before he dumps the Winchesters into something particularly nasty (possibly because Richard Speight Jr, who plays him, has the amazing habit of doing it.)
Angus Deayton's eyebrow soon gained a fan following in its own right on Have I Got News for You. Paul Merton mocked it a lot.
Spock (the Trope Namer) popularized the Fascinating Eyebrow amongst Star Trek fans, though it rarely denoted amusement. Such an emotional response would be... illogical. According to Kirk, it "usually connoted some combination of surprise, disbelief, and/or annoyance".
And another Expanded Universe novel involved Sulu, Chekov, and a random engineer doing an impression of a typical Kirk/Spock/McCoy interaction, complete with Chekov attempting and failing to raise one eyebrow.
Seven of Nine from Star Trek: Voyager would arc her ocular implant when the occasion required, of course, said implant was always in this position so it'd be hard not to...
The Doctor from the same series was a master of it.
Data from TNG, although being an emotionless android, had his share of Fascinating Eyebrow moments.
Captain Picard also did this a few times. In his Nitpicker's Guide series author Phil Farrand jokes that this is a result of his mind-meld with Spock's father Sarek. Vulcans all over Trek are masters at the Fascinating Eyebrow.
In the novel Well of Souls, Talma Pren (a Human) can’t do it, but Vaavek (a Vulcan) can. Talma muses that all Vulcans seem capable of doing so.
Stargate SG-1: Teal'c and the eyebrow are virtually legendary, typically whenever he learns about a new bit of Tau'ri oddity, often accompanied by him saying "Indeed."
The hundredth episode special featured a Show Within a Show version of Teal'c whose actor (or rather the fake actor playing the fake Teal'c on Wormhole X-treme and being played by a real actor on SG-1) apparently couldn't pull off the Eyebrow. There's a shot of him being assisted by a piece of string taped to his face.
iCarly: Freddie can do this. Using it more often on Carly probably would've helped him seduce her by now.
Foreman. It's never a real challenge to get Bingo.
Sylar, especially since Zachary Quinto's eyebrows are so prominent. In the episode "Five Years Gone," when Sylar is using an illusion to disguise himself as Nathan Petrelli, who is president, Zach recorded Nathan's lines so that Adrian Pasdar would know how to say them, but the episode got to a point where Sylar!Nathan cocks his head to the side and stares at Mohinder, but it didn't look right because this trope was missing, since Adrian Pasdar can't cock his eyebrow like that.
Of course, ZQ's ability to do this came in handy when he was cast as Spock in the Star Trek reboot.
When Lucius Vorenus of Rome does this, you KNOW something is about to go down.
Fascinating Eyebrow is one of Agent Scully's trademarks. She would usually eye down Mulder for his crazy theories. It was known among fans simply as "the look".
The Stupendous Yappi who appeared most prominently in "Clyde Bruckman's Final Repose" is a Phony Psychic or Not So Phony Psychic; which one depends really on your interpretation. His eyebrow raise might be considered Exaggerated version. Interestingly, his look was intended to Agent Mulder who for once did not buy his seer routine and thought him a fake.
Earl from My Name Is Earl usually does this when going into thoughts, usually followed by Earl narrating what he did next in that episode. It is actually referred to by characters on the show some times.
Legion also does this during its introductory cutscene. Lampshaded in that he explains the Geth designed his platform specifical to interact with organic lifeforms, so his eye-flaps move to simulate facial expressions.
Legion also does this when you tell the customs officer that the two asari are not Geth because they don't have flashlights in their heads.
Dr. Wily has turned this taunt into a running gag, though he also combines it with a weird sort of eyebrow-wiggle.
Mr. House of Fallout New Vegas is doing this on the picture displayed on his monitor. Since said picture is static, it means he's constantly making this expression.
Webcomics
In Looking for Group, this seems to be Tavor's default facial expression. Unless he's scheming or angry, one eyebrow or the other is almost always raised.
Quite a few people of That Guy with the Glasses are capable of pulling this off. Notable examples: The Nostalgia Critic adds one to his "scheming face" at the end of Suburban Knights, Phelous pulls quite the dangerous-looking one in Kickassia, and Linkara's "I am not amused by this" face comes with it as well.
Western Animation
In Mary Shelleys Frankenhole Jim Belushi desperatly tries to imitate John's trademark arched eyebrow to the point of tying a balloon to it.
Johnny Bravo uses it when scoping out babes, or whenever the events around him confuse him. Considering the likelihood of either one, it's a wonder his eyebrows are ever down at all.
Part and parcel with the more dynamic and emotive designs of Transformers Animated, and not just the humans, either. Ratchet has some excellent ones when trying to understand the younger members of the team, and even Prowl with his highway patrol shades gets in one or two Fascinating Optic Ridge moments, to humorous effect.
In Transformers Prime, with the somewhat more emotive movie based altmodes, Optimus Prime does this, when Miko and Raf lie to him about Bots being involved in street racing.
Used one time by a car dealer on Futurama upon Amy mentioning how rich her parents were. He had to physically restrain it.
In Superman Batman Public Enemies, Lex Luthor did quite an impressive version of this when Power Girl walked into his office with "something to talk about." Given that Power Girl, is, erm, powerful even by DC's standards, one can't help but be suspicious of his intentions.
In Fireman Sam, Station Master Steele's face appears to be stuck this way.
Princess Celestia of My Little Pony: Friendship Is Magic does this near the end of "Lesson Zero", as Twilight's friends are taking the blame for her casting a spell that makes the entire town fight over a doll so that she could learn some sort of lesson about friendship to send her for that week.
Octavia, one of the many fan-favourite background characters, pulls this expression in "The Best Night Ever" when Pinkie makes a request. Even her wiki page uses it.