Subversion in Watchmen: Rorschach considers himself the Only Sane Man, but is batshit insane. In the end it gets double subverted, and it turns out that he was probably right.
Dr. Manhattan is an inversion—he's all but omniscient, but his irregular perception of the timeline causes him to seem insane (sociopathic, at the very least) to people with a regular linear perception of time.
Both Nite Owls are probably the legitimate examples, especially the first one; they realise how messed all superheroes are, including themselves, but can't do anything about it. They're still the most level-headed capes in the book.
In the JLA story arc 'Divided We Fall', several of the League members were split between their civilian and superhero identities. Eel O'Brian, Plastic Man's civilian identity (and former thug), proved to be the driving force that led to the resolution of this situation, as the others either didn't want to return to their superhero identities or were going mad without them. Bruce Wayne, in particular, was growing increasingly psychotic without Batman as an outlet for his rage, forcing Eel to pistol-whip him into submission (which, after all was said and done, even Batman himself considered to be a wise move, given the circumstances).
Basically the entire point of normalman, where norm is the only, um, normal man on a planet full of violent superhumans who quite literally get off on crazy "action scenes". The fact that he's a Deadpan Snarker indicates how well he takes his situation.
In Twisted Toyfare Theatre, Spider-Man is basically the only person in the entire world with a single lick of common sense. However, this has caused him to become so jaded he flat-out refuses to participate in any kind of action if he can avoid it, for example immediately taking the blue pill to go back to sleep when Morpheus offered to take him to The Matrix.
Well, Spider-Man might have company in the "not completely out of his mind" department in Doctor Doom, the series' other main character. Maybe.
Emp, Mindf**k or Maidman also played the sane man amongst the other capes, depending on the situation. So there we have bondage bait with a track record of always losing, a woman who survived torture from her crazy brother, lives alone on a space station and carried out a telepathic affair with another cape, and Batman if he'd dressed as a maid. The Empverse is weird...
I Luv Halloween - Finch, a skull-mask wearing little kid who stuffs razor blades into apples as revenge for getting an apple for Halloween and sets a woman's head on fire, is actually the most level-headed and rational (next to Devil-lad) of the amoral cast of trick-or-treaters.
Astérix and Getafix the Druid are the only two in their town who usually show a hint of sanity and common sense.
The Punisher sees himself as this, in a world where criminals buy, lie, or threaten their way out of paying the price for their actions and superheroes see nothing wrong with battling the same opponents over and over again. Of course, this is also one way of avoiding looking at himself too closely.
Frank: "It's not crazy when the state of the world makes you want to kill everyone responsible. It's crazy when it doesn't.
Some of the more important members of Batman's Rogues Gallery are like this in different circumstances.
The Penguin, as one of the few major Batman villains who is typically considered sane (as such his sentencing would be completed at Blackgate Penn rather than Arkham), serves as this by default. When working with other villains he tends to act as a mediator, defusing arguments and ensuring everyone remains on track; however, he can become exasperated by the "eccentricities" of the other members of Batman's Rogues Gallery, and should he feel that the potential profit of the business arrangement is simply not worth the costs and risks associated with the crime at hand, that his input is being ignored, or that his life and livelihood are being groundlessly threatened by their erratic behavior, there is a strong chance he will wash his hands of the endeavor at his earliest convenience. This goes for the animated series, as well.
If they've really managed to piss him off in the process he'll sometimes spill his guts to Batman in exchange for immunity.
Mr. Freeze is a literal case since he is imprisoned in Arkham Asylum in spite of being mentally healthy because it is the only local penal facility that can accommodate his bizarre medical condition of needing a strongly refrigerated environment to live.
Zibarro from All-Star Superman is a very literal Only Sane Man: He's the only Bizarro on the planet who acts like a normal person, instead of a deranged backwards-speaking manchild.
If you're not aware, Zibarro was what happened when Bizarro Superman decided everyone on Earth should have a Bizarro-clone; Superman lives on Earth, so he has Bizarro Superman, but Bizarro lives on Earth, so he has Bizarro Bizarro: Zibarro.
In Justice League 3000, Supergirl is the only Leaguer who is the real deal instead of a defective replica of the original member. She's a mature, sensible - and snarky - woman and her teammates are a Superman who is an egotistical ass, a crazier-than-usual Batman, a blood-thirsty, booze-guzzling straw feminist Wonder Woman, a deranged Guy Gardner, an annoyingly hyperactive The Flash...
Franklin from the Peanuts comics: he is the only character not to have some sort of quirk or obsession. He is also the only person to point out exactly how weird everyone else in Charlie Brown's neighbourhood is. And - in a twist that was particularly ironic in the late 1960s - he is the only black character in the strip.
Charlie Brown: Franklin! Where are you going?
Franklin: I'm going home, Charlie Brown. This neighborhood has me shook. I didn't mind the girl in the booth or the beagle with the goggles, but that business about the "Great Pumpkin" - no, sir!
Charlie Brown: But...
Schroeder: Hi! Did you guys know there are only sixty more days until Beethoven's birthday?
This is how Sonic feels whenever he's in the Special Zone and how he feels while in Shanazar.
Dr. Caitlin Fairchild, the only one who bothers trying to treat the New 52 version of Superboy like he's not a thing.
In MAD, during the parody of Fatal Attraction, the dog serves as this, objecting to his owner's immoral and poorly thought out actions.
Superlópez: All members of the Supergroup see themselves as this. No wonder they almost wrecked their secret lair fighting over who would be leader.
In Thunderworld #1, one of the alternate Sivanas is much, much more restrained than the others, identifying himself as "a man with personal problems," and is greatly disturbed by his insane and violent (and violently insane) counterparts. There's also the fact that he believed the other Sivanas were going to save the world, not enslave it, so he's pretty much the good Sivana counterpart.
Avengers vs. X-Men was an Idiot Plot of epic proportions. How bad was it? In the main event, Reed Richards was the only member of the cast to suggest that, since the Phoenix Five have made paradise on earth, maybe the Avengers should just let them.
In the Avengers Academy tie-in, both the Academy kids and X-Teens in general display far more sense about the situation than the adults. However it's X-23 who's the first to call out Wolverine on his actions and to make it clear that involving the kids in any way — including by imprisoning the mutants just for being tied to the X-Men — is outright wrong. When Phoenix!Emma later returns to destroy Juston's Sentinel, Laura is also the first to tell her off.
The title character of Dilbert. He's about the least dysfunctional character in the comic and the closest to a genuinely good one.