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Joe in the the flash animations Arfenhouse and Arfenhouse 2 fits this trope.
The titular character in Charlie the Unicorn. It doesn't help that the other two unicorns, apart from their blissful acceptance (if not outright knowledge) of all the strange things that occur around them, are really only minor exaggerations.
Strong Bad, his brother Strong Sad, and Pom Pom on Homestar Runner. Pom Pom is essentially one of the smartest cast members, and often seems to be telling Homestar that everything he's saying is nonsense. Strong Bad, although he causes trouble, is at least smarter than most of his cohorts (and aware that nobody seems to wear pants). As for Strong Sad...
Marzipan also qualifies at times, although this trait is usually overshadowed by her eccentricity and strawman political zeal. Surprisingly, The Poopsmith is the only character who is always depicted as a rational voice of reason (not literally, of course, considering his vow of silence).
Due to the constant gags that render his historical knowledge (which is accurate in terms of our reality) meaningless, Timmy from The Time... Guys could be considered the only sane being in the entire universe.
Church of Red vs. Blue isn't exactly level-headed, but considering the fact that most of the other regular soldiers in Blood Gulch display varying degrees of incompetence or insanity, he's easily the most down-to-earth character present. While this makes him more proactive than much of the cast, it's also the cause of the endlessly irate disposition that tends to overshadow the other aspects of his personality.
Grif would qualify in the respect that he's at least as sane as Church, were he not utterly apathetic to the crazy goings-on of Blood Gulch. Witness his logic in the Warthog argument, which were of course completely shot down by Sarge as being insane and made up. How much of his resulting personality is Flanderization or him just realizing that he cannot make a difference is debatable.
Grif: "The sun never moves around here! Why does no one ever want to talk about that!?"
Simmons has also shown himself to be fairly rational when he's not being a sycophant. One could make the argument that the position of Sane Man among Team Red depends on whether or not Simmons is sucking up to Sarge.
Washington from Recovery One ultimately fits this the best. It actually creates a weird dynamic where Church mocks the others for their stupidity and the Washingtom mocks him.
Again, however, it should be pointed out that in a show where every single member of the cast is crazy or an imbecile, "Only Sane Man" is a relative title. Wash is most assuredly not normal, but compared to everyone else, he's at least mostly all there. In any other fandom he'd be considered a nutcase.
Washington: I'm not crazy, OK? Now if you'll excuse me, I need to go blow up this dead body. (he proceeds to do so. Multiple times. In his defense, he really, really wanted to be sure she was dead.)
Narrator: How do I know if the KGB is watching me?
The Nostalgia Critic: Are these really the type of questions he gets? I mean, why do you need to know this? If the KGB is watching you, there's something wrong with you! Why is the KGB watching you? I don't know! Answer that!
Guy of Life In A Game, being the only "real" person in his video game world, is the only one who questions the insane video game logic that everyone else seems to take for granted. It comes and goes, but the best example of it is in Episode 6-2.
In the first act of A Very Potter Musical, Hermione frantically tries to convince the other characters that the House Tournament is dangerous, but their reaction is pretty well summed up by Harry's line: "Duh, Hermione, I'm the Boy Who Lived, not Died". Later on, in the second act (after Hermione has been proved right), Harry gets a turn: Voldemort has returned, but whenever he tries to talk about it with someone, they change the subject to their love lives..
Dr. Tran fits this trope perfectly, especially when the narrator's around.
Cyd/Codex in The Guild appears to be the only member of the guild in tune with reality. Averted when she arguably goes crazier than any of them, sublimating her real life in the game to the point of talking to her avatar and possibly being taken over by it.
Used in Yu-Gi-Oh! The Abridged Series: The Other Abridged Movie. The Only Sane Man here would be Gary Stu, who can't understand why people are so obsessed with card games - until he falls for them at the end of the movie anyway.
Perhaps due to a Near Death Experience in the previous season ("I CAN'T BELIEVE I'M GOING TO DIE IN A SHOW ABOUT (BLEEP)ING CARD GAMES!"), Duke Devlin is starting to become more or less the Only Sane Man in season 3.
Dan O'Brien from Agents Of Cracked is the only sane main character but is completely unbalanced compared to the periphery characters that are actually normal.
Gordon Freeman as depicted in Freemans Mind is not a sane individual by any standard, but everyone around him is so much more insane/stupid/violent that it's really hard not to see him this way. He even says flat out at the beginning of episode 13 "Everyone is crazy but me!".
The Shark Pooltrailer features one guy whose suggestion for stopping the shark from killing people is to not go into the pool it's trapped in. Everyone else either thinks he's talking crazy, Or thinks its too hot today to not go in.
Spike in the Pony Dot Mov series considers himself this as revealed in PARTY.MOV where after a long conversation with an intoxicated Pinkie Pie he asks himself "Am I the only sane one in this crazy world of technicolor pony weirdos?".
Sasha Hunter in Greek Ninja finds herself rolling her eyes all the time at her comrades' antics.
Algernon's characterization in the Something Awful: Dungeons & Dragons gaming sessions, being dragged into increasingly ridiculous situations with increasingly ridiculous people.
The College Humor page "Facebook History Of The World" has two characters playing this role, one called "Common Sense" and the other called "Hindsight", who are the only ones to realize how idiotic the various historical figures are.
In Ultra Fast Pony, Scootaloo tries (and often fails) to dissuade the other Cutie Mark Crusaders from completely gratuitous destruction. Whenever the subject of racism comes up, Twilight Sparkle is the only voice of reason. And when Twilight Sparkle goes off the deep end herself, Spike tries (and often fails) to talk some sense into her.
In the Noob guild, Arthéon is this as long as you don't mention anything linked to Game Masters or his banned high-level avatar, while the quirks of the other guild members tend to affect their behaviour on an hour-to-hour basis. Ivy, due to her laid-back attitude about things when she's not being hit by a narcolepsy attack, can be seen as that among the female members of the guild then the whole group after Arthéon lets out all that he's been bottling up over the years.
In Relic Tracker's guild, Elyx seems better adjusted than her teammates (the series king of Hair-Trigger Temper, someone hit with Stockholm Syndrome towards him and a Casanova Wannabe) despite a backstory including time in a psych ward.
Turnabout Storm: Much like in their home series, Phoenix Wright and Twilight Sparkle play this role in different ways: Phoenix comes from a mostly realistic setting full of quirky characters, and now has to cope with the weirdness of Equestria plus the quirky characters; while Twilight is the most sensible pony in Ponyville and a constant voice of reason. Much inner snarking ensues with them.
In Welcome to Night Vale, most Night Vale residents are so often exposed to Orwellian government surveillance, eldritch abominations, and supernatural disasters that they don't recognize such events as odd any more. Carlos, a recently-arrived scientist from the outside world, is the only person in the town who realizes just how WRONG all this is.
In Gundam Abridged by Gutted Wren Studios, the role is shared by Sayla Mass and Bright Noa. However, both have their crazy moments; Sayla's moments being set off by any mention of her brother, and Bright's moments by any display of utter stupidity (which occurs often with Amuro around).
In the Lanipator's episode 2 of Abrigimon, Matt was the only Digidestined sensible enough to actually focus on the battle at hand against Apocalymon while everyone else had their own Skewed Priorities.
While the real-life Hitler would be an inversion of this trope, the Downfallparodies' Hitler plays this straight, on some occasions. His life in the bunker revolves around being surrounded by his incompetent generals with useless skills such as drinking, providing trivial information, objecting to plans, pointing at maps, and ranting. They're often the cause of Hitler's schemes backfiring.