Helen: It's just that sometimes you judge people's behavior by a pretty rigid set of standards. Not everyone can live up to them. Daria: That's what's wrong with the world. Helen: Not even you live up to them all the time.
Professor Hwan actually fits this trope obnoxiously well. Always standing around with her fellow scientists in the lab, constantly leaving snide remarks on their part whilst also pointing out their densely inappropriate behavior with nonstop sarcasm.
Nii would probably be more accurate, really; Hwan is more often the victim of the Snark Knight. She's the butt of his jokes most of the time, and generally only manages to comment on their behaviour until he retaliates.
Haruhi Suzumiya: Kyon is this trope in spades. Most of his dialogue revolves around him being snarking over how the world literally revolves around Haruhi's whims.
Haruko Hasegawa of Moyashimon is a dedicated microbiology postgrad with an acid tongue. She delivers a lecture on the validity of "sterilising" products when she sees Oikawa's compulsive disinfecting. Sawaki's supernatural ability to see and interact with (to him) cute microbes triggers a minor meltdown.
In ...Virgin Love, Kaoru's default mode is disdain, which includes disdain for himself whenever he fails to live up to his own standards.
Neon Genesis Evangelion has Asuka, who, at first, does her best to avoid this, but soon can't hold back her rage and angst. Finally, she loses it and has a tirade over why she hates everyone... including herself. Unfortunately, that's not rock bottom — a scarring encounter with Arael and learning Kaji dieddestroy her.
Bleach: Ryuuken Ishida appears to be a bitterly sarcastic individual who is hypercritical of his son's desire and ability to be a Quincy, causing the pair to dissolve into Snark-to-Snark Combat whenever they're in the same room together. Isshin Kurosaki, who knows Ryuuken's secret, implies that Ryuuken is trying to help his son in some very specific way. Flashbacks revealing the beginning of Ryuuken's problems with Quincies show no-one in the world is a harsher critic of Ryuuken than Ryuuken himself. He's clearly a Stepford Snarker, but the link between the start of his problems and his current situation has yet to be fully revealed.
Green Shield/Tara Strong of DC Nation; her genius-level IQ, photographic memory and dedication to her medical studies fulfills the genius requirement and the ridiculously high standards. She's also quicker with the snark than she is with her bow.
Bastille from Alcatraz and the Evil Librarians is, in fact, a knight. With snark.
Greg Heffley from the Diary of a Wimpy Kid series would qualify as a male Snark Knight, if not for the fact that he usually doesn't hold himself to his own standards. Heck, he even says that his only New Year's resolution is to come up with resolutions for other people, since he's the best person he knows.
Doctor: You're a cynic. Benny: No, I'm an idealist who's been wrong one too many times.
Christina Light in Henry James's first novel Roderick Hudson. Speaking to Rowland Mallet, she says:
"I am a strange girl. To begin with, I am frightfully egotistical. Don't flatter yourself you have said anything very clever if you ever take it into your head to tell me so... I am tired to death of myself; I would give all I possess to get out of myself; but somehow, at the end, I find myself so vastly more interesting than nine tenths of the people I meet."
Dominil finds herself firmly in Snark Knight territory in Curse of the Wolfgirl. Daniel likes to think of himself as one, but he is too firmly mired in the chaos to be one.
In Babylon 5, Londo's first wife Timov falls into this. Even though she's constantly (and justifiably) berating him, he chooses to keep her over all his other wives. He's suspicious of all flattery, but he knows her contempt is genuine.
April Ludgate the college intern is another prime example. Season 2 has April starting to get over it, though, beginning to distance herself from her irony-loving friends and getting more involved in the department. She still provides a healthy dose of snark, particularly towards Jerry, the office Butt Monkey.
Major (later Colonel) Kira Nerys was the heavy-handed embodiment of this trope, just like Ro Laren before her. Almost to a "Can't Argue With Bajorans" extent. The role was originally written to be Ro Laren, as was the character B'Elanna Torres in Star Trek: Voyager.
Veronica Mars: Veronica takes this role but unlike most, only after she's been pushed into it by her ostracization for standing by her father. Note her moral principles fall into a sense of justice and not letting the wealthy get away with crimes but she's loose on using deception to get her way. Such is the way of most Private Detective characters.
August Leffler, Tommy's ex. August either went through character decay (or development; as a teenager, such a change in personality isn't unrealistic), becoming rather hypocritical and just liking to look down at everyone. Her initial apperance portrayed her as a more well-adjusted and pleasent person (At least, as well adjusted as The Snark Knight can get).
Tommy himself could be considered a male Snark Knight, although to a much lesser degree than August.
Kerry from 8 Simple Rules usually fits, though it can depend on the episode.
Naomi from the second generation of Skins characters; arguably Jal has flashes of this in the first two seasons too.
Degrassi rotates this trope around through the years. Ellie is the first notable example during her goth years, Jimmy gains this along with Disabled Snarker title, Clare being the latest holder of this title.
Toby Ziegler from The West Wing — he's accurately described as "prickly" and "sad, angry and not warm," and he has a uniquely tense relationship with the president due to his constant frustration and disappointment at Bartlet's failure to fully live up to his genius, and his willingness to voice them.
Doctor Who: The Doctor has a very dark and twisted version of this in the Dream Lord, from Amy's Choice. Even as he traps the heroes in a dream and toys with them, he snipes at all of their character flaws, with particular venom reserved for the Doctor. He's actually an extension of the Doctor's psyche, particularly his darkness and self-loathing, which qualifies him for this trope.
Dan from Nathan Barley is a Deconstruction of the trope, penned by Charlie Brooker (himself arguably a Real Life example). He's a caustic depressive who writes withering articles about "the idiots" (who themselves respect him as "the Preacher Man"), growing more and more cutting and vicious as he falls in with them. However, when he's offered a job for a more reputable magazine, he realises he cannot write anything but cheap sarcasm, and it's hinted that his self-deprecation forms a self-destructive cycle; the show offers him plenty of get-outs, but he never ends up taking them.
Malcolm from Malcolm in the Middle takes the cake. Always, always snidely fuming at everyone and everything. A couple episodes try to tackle this directly (with him trying to suppress his desire to grumble and condescend for various reasons) but ends up blowing up in his face (he gave himself an ulcer once by swallowing down too much snark).
Ryan King (played by Matthew Perry on Go On) is definitely a big example. He also is something of a Stepford Snarker.
Squall Leonhart of Final Fantasy VIII. He's aloof, unfriendly, and periodically quite snarky, and if anything holds more disdain for himself than he does for others, mostly expressed via Inner Monologue.
Although there is never exactly one interpretation of a Touhou character, Patchouli Knowledge is usually portrayed as a Snark Knight. The games show her as completely deadpan and cynical (especially in her lines regarding Sakuya in Subterranean Animism or Immaterial and Missing Power), but nevertheless a good and caring friend of Remilia, and fanon often shows her as having a crush on Marisa.
Jacqli of Ar tonelico at first appears to be a Jerkass willing to betray anyone to accomplish her mysterious goals, and bitingly sarcastic towards everyone, especially the protagonist (also a Deadpan Snarker) but over time, as she comes to trust the heroes, she reveals her goals truly are noble that are simply hidden behind a hostile exterior because she is embarrassed to be working towards such goals, and distrustful of others.
Shadow the Hedgehog from the Sonic the Hedgehog series. He's got goals, generally involving being the best (just like Sonic, which is why they clash so often). And he prefers to fulfil these goals on his lonesome. His only real friend is the robotE-123Omega.
Bully's Jimmy Hopkins serves as a slight subversion of this trope. He understands how crooked the school system can be with the various cliques and corrupted officials. He starts off the game as simply wanting to be left alone, but eventually transforms more into a Knight in Sour Armor.
This is an option in the Mystery Case Files PC game Dire Grove. On the main menu, you can toggle whether you want the Player Character's internal monologues to be Normal, Motivational, or Snarky.
Another Tales example, Yuri Lowell seems to have a sarcastic quip for just about any situation.
Red vs. Blue: This is Church. He even crosses into outright (attempts at) heroism sometimes, but never ceases pointing out how stupid everyone around him is, especially Caboose. He also has a strange sort of enduring optimism, in that he can be compelled to genuinely try to help people he likes. Washington from Reconstruction almost fits too, but...
Aggie of Penny and Aggie starts off this way. Early storylines see her standing on the sidelines and aiming sarcastic comments and the occasional prank at popular girl Penny for her apparent superficiality and snobbery, in contrast to Aggie's espoused (though not always upheld) progressive values. She's also initially something of a loner with only one friend, the bookwormish Duane. Eventually, she develops a wider circle of friends, including Penny herself.
Tristan of Angel Moxie. A pretty cynical youth — especially of anything she perceives as "girly", thanks to her extreme tomboyishness. Her mother is utterly desperate for Tristan to display even average teenage behavior.
Karkat hates everyone, including himself. (At one point he thought he was his own hate-soulmate. It's a troll thing.) He insults everyone mercilessly, again including himself. His ability to rag on himself is aided by the time travel tomfoolery that all the trolls are up to their bulge in; he constantly gets into arguments with his past/future self. He also happens to be the Knight of Blood. Despite his bluster it's worth listening to him, as Karkat has a good measure of people and can point out their flaws accurately.
Rose. Pretty much 90%+ of everything she says is sarcastic, either playfully so or biting. Part of this comes from a childhood of passive-aggressive antagonism with her mother — except even that may have been one-sided and an illusion caused by Rose viewing her attempts to bond through Jade-Colored Glasses.
Daria: Daria Morgendorffer. Formerly a minor character on Beavis And Butthead, her derisive comments on the stupidity of the title characters made her popular enough with the fans' own sense of teenage world-weariness that she got her own show. She used to be the Trope Namer.
Noah definitely falls into this category, since that was his only distinctive trait in season one, with Duncan coming in at a close second. Now that it's been 3 seasons, Noah's fleshed out more, but is still definitely a snarker when he wants to be.
Gwen also qualifies, especially in the first season.
Brendon Small of Home Movies comes close. His ruthless self-criticism applies only to filmmaking, not any other aspect of his... uh, does Brendon have a life?