Jack: I don't do these things just to drive you crazy, Lemon. I do them for the good of the show. Liz: Well, I'm the one who always has to clean up the mess afterward. Jack: That's why my job is way better than yours.
Rossiu, from Tengen Toppa Gurren Lagann, after the timeskip, is the only one in the Dai-Gurren Junta (with the possible exception of Leeron, who just wants to do Science!) with any ability to run things. At all. Seriously, they're shocked by his development of standardisation and law courts. It might just be because he's the only one who grasps the concept of sitting down and thinking about things, rather than just running off to blow something up. Of course, when he takes it too far, their complaints began to make sense...
Riza Hawkeye in Fullmetal Alchemist. She's constantly picking up the work left behind by her boss Mustang and telling him and the others off for not doing their work- all with a long-suffering, exasperated expression on her face.
Mina Murray in The League of Extraordinary Gentlemen. She even states that she is "In charge of this menagerie." Well, when your team consists of an old opium-addicted hunter; a science-pirate; an insane, lecherous invisible guy, and a wussy doctor who can turn into a rampaging behemoth, 'menagerie' is the only word to describe it. She takes it to the point that she's the de facto leader of the group, as she's the only one normal and grounded in reality enough to actually keep them together and pointed in a relatively useful direction.
In Stranger Than Fiction, Karen Eiffel is given a personal assistant to help her out with writer's block and make sure she finishes the book (key word: given). She does not want a personal assistant, and she does not want to be forced into finishing her book, she just wants to let it happen organically. Her publishers, on the other hand, want another book to sell.
It's unlikely the listing for the "cemetery caretaker" job in Cemetery Man mentioned having to stop the living dead from escaping the graveyard. Hell, the town doesn't even pay for the bullets.
In Discworld: Pretty much the duty of the kelda in any clan of Nac Mac Feegles.
Also at Unseen University where this role is filled by Ponder Stibbons, the Archchancellor or the Librarian, depending on what job needs doing. Rincewind is also an example, as after his running days are over, he seems to accrue any title no-one else want. (At one point, it's shown that Ponder has taken on so much extra work - which the senior wizards were happy to pass off to him - that he actually the controlling stake in running the University.)
The Bursar tried hard to be one of these before he required dried frog pills, but the Archchancellor proved a bit too much for him to handle.
Vetinari as well, not so much the only sane man, but the most sane one. An example turns up in Jingo, surrender was the most logical course for Ankh-Morpork from the very beginning, but only Vetinari is able to see it.
The Last Hero states that for any organization to survive, it needs at least one person who is this.
In Maskerade, Salzella appears to be this at first, but by the end of the book...
To a lesser extent, Pete from the same show, as he has to take care of Liz when she goes off the rails herself, as well as (apparently) dealing with the NBC pages. Although in later seasons, Pete seems to be going off the deep end himself, more so than usual.
Possibly the title character of Ugly Betty. She babysits her boss 24/7, but she often comes to rescue of everyone else in the main cast, including the ones who treat her badly, not to mention the times she saved the entire magazine.
Also the titular character of Yo Soy Betty La Fea, who, while not exactly babysitting her boss, seems to have internalized that "Secretary of Presidency" actually means "make all things possible so the boss don't screw it up his job", doing things from shielding the boss' fiancée from finding about his sexual escapades (and distracting the exes so they don't reach the man), to actually creating a full finances plan with a healthy dose of fiscal trickery so the company don't goes bankrupt under her boss' administration.
Michael Bluth from Arrested Development. Even worse, the insane people are his family, so he has to cope with them 24/7.
Jen in The IT Crowd — in fact, the first episode has her appointed head of I.T. by the semi-sane CEO, Denholm Reynholm; despite her lack of computer knowledge, she realizes her people skills would help raise the status of the department. Some episodes play with this by having her go completely off-the-rails over something which, although apparently more 'normal' than the geeky lifestyle she is surrounded by, she goes really overboard in taking seriously, leading to Roy or even Moss having to hold the sanity ball.
Ted Crisp from Better Off Ted, head of R&D for Veridian Dynamics - when he's not helping Lem and Phil with their problems he's keeping Veronica from doing something even more blackhearted than the last blackhearted thing she's done or "totally not flirting" with Linda.
In Primeval, Captain Becker is flat-out told that this is his job description. Babysit the scientists, don't get sucked up in their insane theories, don't let them get themselves killed, and, if he has time, review the security of the base.
Kermit the Frog, although he even subverts it: "Me not crazy? I hired the others."
Scooter is one to a lesser extent when he isn't being pressed-gang into one of Miss Piggy's schemes, often remarking on how insane their coworkers are. Sam the Eagle likes to think he's the only sane one involved in the production of the show, but he is very mistaken.
Also Principal Figgins considering some of the crazy and demanding teachers he has to deal with.
Coach Beiste has fallen into this role, occasionally even realizing that she is working in an insane asylum that masquerades as a high school.
Cuddy in House. It's even lamp-shaded by Chase once when she goes off the rails: "Stopping the madness is her job!" "Somebody's gotta be Cuddy's Cuddy."
On Bones, it was FBI Agent Seely Booth's job to work with the no social skills "squints." Then Dr. Camille Saroyan was hired to oversee them all (including Dr. Temperance Brennan, despite what Brennan may think sometimes) so she can be this.
Clark Edison, one of the interns, also falls into this category. He prefers a professional environment, often expressing annoyance when the topic of conversation switches from investigation to the episode's side-plot. Which makes it all the funnier on the rare occasion that he joins in, and the others think that his reaction is 'too much'.
Lt. Fick of Generation Kill seems to be the only officer in the battalion with much interest in actually surviving the invasion of Iraq. In addition to leading his own eccentric Blood Knight platoon, he spends a large amount of time making sure the other officers don't get their platoons killed.
However, somewhat averted when you look deeper into the source material: most of the company commanders were untested in combat, and falling back on their training and what little experience they had. In fact, one company commander's assistant, who was viewed as a brown-nose by all the men in the company, actually turned out to be one of the most competent and respected commanders when he was promoted.
On The Office (US), the employees at Dunder-Mifflin can be grouped into "sane" and "insane", although this definition is fluid and many characters have drifted over time. Notably, many characters who started out very sane have since dove off the deep end (Jan, Ryan, and Toby, though he recovered). Some characters who are insane have flashes of sanity or at least competence (Michael, Angela, Andy, and even Dwight), and some characters are sane but helpless (Phyllis) or apathetic (Stanley, Darryl). Jim and Pam are usually portrayed as sane, though sometimes they let their flights of fancy get the better of them, and, as a recurring theme, whenever Jim finds himself in a leadership position, he is far less competent (since his worst fear is "becoming Michael"). By far the most rational, level-headed character in the office is Oscar, and in more recent seasons he has taken to pointing this out repeatedly. (He cites himself, Jim, Pam, and Toby as the "coalition of reason", and when Jim and Pam took their honeymoon, complained that the ratio of sane-to-insane employees was disrupted.)
While Oscar is often shown as having more knowledge than anyone else, the job of looking after the insane characters falls squarely on Jim's shoulders. He had to defuse Michael's and Dwight's schemes for years. The clearest example is when he goes along as they prank another company branch, because left to their own devices they would have used explosives. Oscar sometimes gives background comments, but he never misses work time to do damage control.
In the final season Jim manages to trick Dwight into acting as his own Only Sane Employee. Dwight gets promoted to manager and Jim is the assistant to the manager. However, he convinced Dwight to also assume the role of the assistant to the assistant to the manager. This means that when Dwight has a crazy idea, he passes it to be implemented by Jim who passes it right back to Dwight who then realizes that it is crazy and abandons it. This works so well that by the end of the series, Dwight becomes a rather competent, reasonable and sane manager. This plus some selective firings has the extra effect of reducing the level of crazy in the office by a massive amount
Played with to the point of inversion in the British version, where so far as can be determined most of the employees are reasonably sane (with one or two exceptions, such as Gareth); they just happen to be managed by a deluded, egocentric Attention Whore.
Poor, poor Paul Lewiston and Carl Sack in Boston Legal. Shirley Schmidt is usually this in regards to Alan and Denny, and is the serious, sober face of Crane, Poole and Schmidt, but seeing as how her first appearance onscreen was an innuendo-laden bit of banter with Alan Shore in the men's room, well...
Ally and Georgia were more or less this in Ally McBeal - though Georgia was clearly the more level-headed as Ally is completely bonkers in her personal life. This may be why Georgia was often paired with Richard in cases, trying to drive sense into a guy who was in it to make money and destroy the law as a bonus. By contrast, Ally usually worked well with John because she was the only one who understood his neuroses.
Laura from The Brittas Empire. Most of the problems come from Mr. Brittas, but the other staff are plenty dysfunctional too.
Chuck Bartowski from Chuck is this... at least he is at the Buy More, not so much at his other job though.
It's due to this trope that he's the Almighty Janitor. Chuck is really the one who runs the Buy More.
Daníel from Naeturvaktin is the only regular character who can do a decent job. His boss is a dictatorial bully who offends every customer he meets, and his only co-worker is a ditz who's usually either slacking off or (incompetently) trying to make his fortune in showbiz.
In Game of Thrones, this is the role of Hand of the King. It's even lampshaded in the first episode;
King Robert: Lord Eddard Stark, I would name you The Hand Of The King.
Ned Stark: I'm not worthy of the honour.
King Robert: I'm not trying to honour you, I'm trying to get you to run my kingdom while I eat, drink, and whore my way to an early grave!
In the books, there's an actual saying in Westeros "The King eats and the Hand takes the shit". The series renders this as the more accurate, though somewhat less poetic, "The King shits and the Hand wipes."
Tyrion and later Tywin both take this role when serving as Hand of the King for King Joffrey. Dealing with insane kings isn't particularly new for Tywin, who had previously served as the Hand for Mad King Aerys.
Trudy in House of Anubis does the actual day-to-day running of the house with no help from Victor whose only concern is keeping his secrets secret.
Castiel in Supernatural often comes across as the only sane Angel in the heavenly choir.
With all the eccentrics in his team, Gibbs from NCIS does seem to be running a daycare centre instead of an investigations unit sometimes.
Ken Cosgrove in Mad Men is one of the few people at Sterling-Cooper without some crippling character flaw or big secret. He's the only guy to complain about safety before the infamous lawnmower-meets-foot incident, and the first to call for an ambulance after. Pete has to use his wife's connections to sell a short story, and Paul's one-act play screams Her Codename Was Mary Sue, but by season five Ken has quietly published over 20 stories under a pen name - and is embarrassed when his colleagues find out.
The complete aversion of this trope is what makes Community so funny. The Dean and professors of Greendale are just as insane as its students.
And when those who once tried to keep everything under control (Dilbert, Wally and Alice) flat out gave up and started exploiting the system for their own personal gain.
Asok the intern would have this job; he has the right perspective and opinions to play this role, but he has no seniority and therefore nobody pays any attention to what he has to say. He shows every sign that his Only Sane Employee nature is an aspect of his inexperience, and he'll be broken of it long before he's been there long enough for anybody to listen.
He has started taking lessons from Wally.
Everyone in Retail who's on the lowest rung of the corporate ladder seems to be pretty sane. Store manager or above, not so much. Subverted with Marla, however, since her promotion; she seems to be retaining her common sense, at least so far.
Inverted Gaston Lagaffe: Gaston is the only dysfunctional employee, but he is crazy enough to turn everyone's job into this trope. Fantasio (and later Prunelle) spends most of his time trying to get Gaston to work. And then when Gaston tries to work, he just screws it all up.
In any game, in nearly all gaming groups, there WILL be one of these among the players/Dungeon Master.
The premise of the casualMiss ManagementTime Management Game. Every NPC employee comes with a set of weird quirks; the player character is the manager, and the main aim is to keep the staff from having nervous breakdowns while somehow getting enough work done to finish the level.
If you take your shirt off in Metal Gear Solid 3: Snake Eater and call SIGNT, Snake will ask if he can take off his pants. SIGNT reacts in disgust and wonders if he's the only sane man of the unit. For the record, the rest of the unit consists of a British officer obsessed with James Bond and his own Britishness, a doctor obsessed with B-movies and cloning, and a veteran soldier obsessed with eating everything that moves.
In many MMORPGs, a more experienced player in a group will often be put in these positions. The real challenge isn't in fulfilling their own role, rather keeping others from doing overtly stupid things.
In Fire Emblem: Path of Radiance, the Crimean army is almost entirely made of nutcases, with trusty right-hand Titania and stern strategist Soren the seemingly only persons to do any work outside of fighting. Captain Ike has said explicitly stated he couldn't do anything without them. Then again, there was this one exchange about storming an enemy fortress in which Soren succumbed to the craziness and Ranulf was the Only Sane Man left. It went something like...
Soren: Door's open. This is almost certainly a trap.
Ike: Hm. How about we all barge in through the front door?
Soren: Probably the best course of action. Let's go.
Ranulf: Errr, guys?! Isn't this the part where we stop and carefully consider strategies?! No? (Sigh.)
In Star Wars: The Old Republic, Light Sided Imperial players tend to come across as being this for the Empire. In-universe, Keeper claims that this is Imperial Intelligence's real job, to just let the Sith do their thing and the military go ahead and play soldier, while Intelligence cleans up the mess they leave behind and keep the Empire actually running in the meantime.
The eponymous Digger ends up having to do this with, to be honest, nearly everyone she meets in this webcomic, although it's implied the Statue of Ganesh and Boneclaw Mother keep their respective flock/tribe in line.
Stan, especially since season 6. His extremely frequent catchphrase gesture in any situation in which he is forced to play Liz Lemon (usually to a bunch of adults), he will squeeze his eyes tightly shut and pinch the bridge of his nonexistant nose in one of the most expressive and dead-on displays of utter exasperation ever witnessed. Often accompanied by a muttered "Oh goddamnit..."
Kyle as well on occasion, as long as it has something to do with Cartman.
Charles Foster Ofdensen in Metalocalypse is what happens when a Liz Lemon takes a level in Badass. He and the band have both stated that it is understood, if not directly outlined in his job description, that part of his job is to talk them out of bad ideas they think of when they're drunk (not that they can't think of bad ideas when they're sober), meaning that this trope is almost his literal job description. Further evidenced in the opening episode of Season 3, in which the band almost goes bankrupt due to spending money too recklessly in his absence.
Hank Hill in King of the Hill, especially in the later seasons as his co-workers grew more and more quirky. Also, his role in his group of friends. Things tend to deteriorate rapidly when Bill and Dale (sometimes Boomhauer) are left to their own devices. Consider the episode where Boomhauer accidentally gets committed to an asylum because the people in Houston can't understand him. He calls Dale, who ends up there too (he tried to sneak in as if he were a secret agent), and he calls Bill, who checks himself in voluntarily. Finally, at this point, the grudgingly admit they need Hank, who gets the matter resolved in minutes.
Lana Kane of Archer, especially in the later seasons.
The Assistant Director's job on a film is to be this to the crew. The Director is the one who manages the actors (so this to an extent) and has the final say, it's up to the AD to keep the whole shoot organised. In fact, ask anyone who has ever been involved with directing a production of any sort; they will be the first to tell you that their job is to keep track of everything... including the director's head. And probably his sanity as well.
Any real life Stage Manager in the theatre or for a band. Their job description is literally "make things run smoothly."
High school choir director/musical theater directors tend to this. Dealing with 50 or so eccentric and hyperactive teenage singers every day is the Liz Lemon Job of Liz Lemon Jobs.
Occasionally an employee will be hired for common sense rather than for technical skill. This employee is usually in charge of some business that involves lots of technical skill but whose employees are mostly without common sense. For example, computer engineers usually have much technical skill but little common sense so an executive with common sense is hired to oversee them and make sure they don't do unnecessary things. ("But if we overclock the server, we'll be able to maximize efficiency by streamlining the process and-" "Not if it explodes." "Oh. Right.")
And quite often, the employee with the actual technical skills will feel like this as well. ("What you're asking for is physically impossible." "But we already promised it to our customers! Can you fix it anyway?")
Office Administrators. Especially in settings where they work alone (meaning, no personal assistant or junior secretary) and are therefore the only ones capable of doing their jobs.
Avoid this kind of work at all costs. It combines low pay, high responsibility and unfortunate accusations of "attitude problems" if you give any hint you are aware of the first two to your colleagues.
Albert Speer was this to Those WackyNazis: someone who wasn't a delusional megalomaniac (Hitler), a self-indulgent junkie (Goering), a crazed fanboy (Goebbels) or all of the above (Himmler). His organizational skill and grasp of reality were largely to blame for the fact that the Third Reich lasted as long as it did (he achieved questionable Karma Houdini status thanks to a half-hearted attempt to assassinate Hitler, by the splendidly appropriate means of poison gas.)
Heck, his status as Only Sane Man is probably responsible for his Karma Houdini status, since while the others remained completely insane, blinded by ideology, crazed by drug abuse or some combination thereof, he was one of the few who recognized in advance that the war wasn't going to end well for the Nazis and that it was probably a good idea to make sure you could plausibly come out the other side in one piece. The fact that he was the only one out of the Nazi High Command to express any kind of regret or remorse for what had happened probably helped spare his life as well.
In more recent years, Keiji Inafune seemed to serve this role for Capcom, being quite possibly the only employee there who both wanted to do something other than turning Capcom Sequel StagnationUp to Eleven and had the ability and clout to do so. (In fact, Lost Planet and Dead Rising were facing cancellation more or less for not being a sequel, so Inafune intentionally made their "demos" go way over budget for the sole purpose of being able to say "we've poured all this money into it, why cancel it now?") Then he resigned from Capcom because he didn't want to spend the rest of his career making half-baked sequels. In no time flat, Capcom made a series of questionable decisions, each of which managed to annoy fans more than the last, culminating in a massive Internet Counterattack in response to the cancellation of Megaman Legends 3.