In the same vein as Batman, Zuko's perpetually frowning, serious demeanor leaves him wide open to many a humorous moment, partially to being paired with his foil of a jolly uncle.note Hilariously parodied in this comic. Subtly acknowledged later in the series when Sokka asks Zuko if he's happy now that he's foiled Sokka's plan, and Zuko replies, deadpan, "I'm never happy." Sokka and Zuko work together in this role almost as well as Zuko and Iroh.
Sokka started out as a stern, down-to-earth, warrior-in-training, but his Comically Serious moments, as well as improvisations from his comedian voice actor, soon turned him into a goofy Plucky Comic Relief. Also see him trying to work with a bunch of out-there "nomads" in "The Cave of Two Lovers".
Azula: That's a sharp outfit, Chan! Careful, you could puncture the hull of an Empire-class Fire Nation Battleship, leaving thousands to drown at sea! Chan: ... Azula: Because... it's so sharp!
In The Legend of Korra, Korra's airbending teacher Tenzin takes on this role. He doesn't think that the shenanigans going on around him are at all funny, which of course means he becomes the target of endless inconveniences and humiliations. Also becomes a case of Not So Above It All.
Amon has shown potential to be this too if the memetic "Comedy Amon" is any indication.
Even in the Grand Finale of Justice League Unlimited, where he threw himself hopelessly at a villain who could take punches from Superman, he was laughing at the Bat's sheer tenaciousness. Of course, in lieu of better ideas, which is what Batman normally does, what else was there to do?
Who can forget the ending of This Little Piggy when Batman is forced to sing? And actually has a great voice!
Zatanna: And you'll keep your part of the bargain? Circe: A deal's a deal. He can stop now. Zatanna:Not on your life!
In "Kid Stuff" when the Justice Leaguers are de-aged into childhood Batman still keeps up his grumpy demeanor. This becomes actual unfunny at the end of the episode, when he reminds the others that he was regressed to the age he was when his childhood came to an abrupt and unhappy end.
A rare Batman laugh came when Harley Quinn told him how The Joker will love her for successfully putting Batman in a Death Trap. However, it was more an Evil Laugh meant to freak Harley out.
Ben 10 (2016) is a Denser and Wackier reboot of the original, meaning that even the villains that are still dangerous have some kind of funny quirk. So when Vilgax (who is virtuallyunchanged from his original characterization) has to deal with the likes of Zambozo or Animo, it's usually comedy gold (until it's not anymore).
Bob's Burgers: Bob Belcher and his emotionless daughter Tina. A major part of Bob's character is that he reacts to the insanity around him the way a Real Life person would.
Daria has just about enough dry humor and witty remarks to qualify as this. Made even more hilarious by the fact that she manages to maintain her dispassionate expression. This is especially evident in the episodes' promos with Jane before the intro of the show.
The central premise behind Droopy was the fact that he never raised his voice, or ever sounded interested in anything. One of the character's Catch Phrases was "You know what? I'm happy." He would say this in the most deadpan, uninterested tone possible. Until you ticked him off sufficiently, but even then the No-Holds-Barred Beatdown was prefaced with "You know what? That makes me mad." in the same deadpan tone as the previous line.
Dijon from the 2017 Ducktales 2017 reboot is a perfect example of this. Pretty much every single one of his lines is delivered with a stern expression and dramatic flair, inspiring Dewey to also start making overdramatic speeches through the episode. He is also fairly gullible in taking everything 100% seriously, to the point where when someone does the "Got your nose!"-trick on him, he actually believes they stole his nose and draws his sword to demand it back.
This is all Adam Westing, since he's known in Real Life for being comically serious (a not wholly undeserved reputation). He's even made jokes about it himself.
Agent Powers and Agent Trigger from the Gravity Falls episode "Scary-oke" are a pair of stone-faced MiBs who end up investigating the weird goings-on in town. Powers claims to be physically incapable of experiencing laughter, while Trigger has a tendency to dramatically repeat the last word his partner says, and does things like confiscate an armful of "Mr. Mystery" bobble-heads for "evidence".
Dipper certainly has his moments. Anytime he attempts to look smart and mature, expect it to be ruined by Mabel's or Soos' antics or his own hidden goofiness.
Hank Hill, of King of the Hill. In addition to playing the Only Sane Man amongst his bizarre circle of friends, his hyper-mundane personality is often a source of humor in its own right.
Benson from Regular Show. He HAS a sense of humor, and he's lightened up over the course of the show, but he can be very uptight, angry, and many of the things listed in the above example. Even when everything going on around him is hilarious, he'll still be red-faced and screaming. "GET BACK TO WORK OR YOU'RE FIRED!!!"
Samurai Jack himself. Whether polymorphed into a chicken or sporting an eye-popping rave outfit (complete with a pacifier), he still manages to maintain the same determined expression.
The episode "Brother From Another Series" revealed that this trope is why Sideshow Bob became Krusty the Clown's sidekick instead of his brother Cecil. As Krusty explains after a poor pie-in-the-face gag from Cecil's straightforward goofy clown audition:
Krusty: Free comedy tip, slick: the pie gag's only funny when the sap's got dignity. (sees Bob) Like that guy. Hey, Hal, pie-job for Lord Autumnbottom there!
Bob then gets hit in the side of the head with a pie, causing his huge, bushy, palm-tree-like hair to spring out of his hat and everyone else to die with laughter.
Principal Skinner as well.
Reporter: Principal Skinner, you've been referred to as "the funny one." Is that reputation justified? Skinner:[seriously] Yes. Yes, it is.
One episode had the family visiting a comedy club. One of the comics, with a dreary expression on his face that never changes, walks up to the mike and simply says: "I finally got around to reading the dictionary. Turns out the zebra did it." (Homer is the only person who doesn't laugh.)
Rex Banner who's brought in to enforce Prohibition. He's physically unable to laugh, even at his own jokes.
Shadow again takes this role in the last first-season episode of Sonic Boom, where he takes the goal of killing Sonic way more seriously than the overly giddy to work with him Dr. Eggman. He also sounds completely serious when he claims Sonic's poor attempt at building a bookcase earlier in the episode is reason enough to justify murdering him.
Shadow: Your shoddy craftsmanship brings shame on all hedgehog-kind. And for that, you shall perish!
Garnet. Silly things sometimes happen to/around her and she never stops being serious. Case in point, in "Together Breakfast" when fighting a monster made from a demonically-possessed plate of waffles she says, completely seriously, "Now it has all the powers of a breakfast. We have to destroy it!" In "Pool Hopping", she wants to be able to look into unlikely futures, and reasons that to do this, she has to be random and unpredictable. A lot of humor is drawn from Garnet acting ridiculous and being deadly serious about it.
Steven: Uhh, Sapphire? The toilet's frozen. Sapphire: Such is fate. Steven: Am I fated to pee outside in the grass too? Sapphire: Yes.
Peridot, at first. She first assumes that "Steven" is the name of a species that replaced humans, and still thinks the sticker she saw at the Galaxy Warp is an official symbol of some kind. As she starts to lose it from isolation, this trait diminishes, such that by "Friend Ship" she spends the entire episode laughing like a maniac and gleefully tormenting the Crystal Gems. This trait swings around to full prominence in "When It Rains", where she delivers a serious, calculating monologue about trusting Steven after he... explains the water cycle to her.
Lapis has her moments thanks to a lack of social skills. When she first leaves Earth to go back to Homeworld, a dramatic exit is ruined by some awkward pauses:
Lapis Lazuli: Thank you, Steven! Steven: No prob, Bob. Lapis Lazuli:[beat]It's Lapis... Steven:[beat] ...Yeah. Lapis Lazuli:[beat] Okay, bye.
Yellow Diamond as well, as being called a "clod" by Peridot provokes a hilarious reaction.
As opposed to his originalsource, Shere Khan in TaleSpin is a master of this trope. No matter what insanity is occurring around him, Khan responds to it in the exact same deadpan growl as he uses during a regular business meeting. In fact, if Khan ever smiles at you it's probably a good idea to run like hell.
Optimus Prime has shades of this in Transformers: Prime. Bulkhead explicitly mentions never seeing Optimus laugh, cry or lose his cool, but funny stuff is made funnier by his completely deadpan reaction to it. After showing a LOLCats-esque internet meme that actually got Ratchet to chuckle, Jack asked Optimus if he wanted to see something funny, Optimus replied rather bluntly "No."
In another incident, Optimus is called upon by Agent Fowler to talk to his superior General Bryce in order to alleviate some tension regarding recent events. Given that Bryce and the camera-man were not expecting Optimus to literally be outside their window, it results in them acting befuddled talking to a 30 foot robot. Optimus meanwhile remains courteous and polite the entire time.
Another giant robot with no sense of humor is the Decepticon Lugnut from Transformers Animated. Luggy is a gigantic and merciless war machine with a completely serious and fanatical devotion to his lord Megatron. As opposed to his more eccentric partner Blitzwing, he never, ever jokes. He's also often hilarious.
As Transformers: Rescue Bots is in the same continuity as Transformers: Prime, it should be no surprise that this carries over to Optimus Prime's portrayal in that series as well.
Blades: Helping you is... Well, you're bigger than Elvis! Optimus: I have not met this Elvis and am unaware of his size.