Dumbledore: You may have noticed a few changes around school? Harry: A FEW! WHAT THE BLOODY HELL HAPPENED WHILE I WAS AWAY? WHERE'S EVERYONE'S BLOODY CLOTHING? ARE YOU ALL MAD!? Ron: 'arry, that's just not polite.
You're giving me a time machine to treat my sleep disorder.
You're giving me a TIME MACHINE to treat my SLEEP DISORDER.
YOU'RE GIVING ME A TIME MACHINE IN ORDER TO TREAT MY SLEEP DISORDER.
"Ehehehehhheheh..." Harry's mouth said. He was now holding the necklace away from him as though it were a live bomb. Well, no, not as if it were a live bomb, that didn't begin to describe the severity of the situation. Harry held the necklace away from him as though it were a time machine.
Played With, in that the rest of the characters are perfectly normal, and Harry is simply significantly more sane than the average person.
In the Disgaea fanfic Disgaea Jewel of the gods Adell is this, due to Laharl and Mao often arguing all the time, or being crazy.
Mao is this when Laharl and Adell are being too Hot-Blooded.
Played straight in Bagenders with Legolas (and possibly Sam), Aragorn being somewhat neurotic, Frodo being insane, Gandalf being a Dirty Old Man, as are Merry and Pippin, Gimli is rarely seen, but has installed anti hobbit defence mechanisms in his room.
Of course knowing the crap that Merry, Pippin, and Frodo do that's an example of Properly Paranoid.
Zuko in the Avatar The Last Airbender fanfic The Boiling Rock definitely fits it. If he's not breaking the Fourth Wall, he's mentioning how the story is nothing but a world of madness that he is trapped in.
SORA: AM I THE ONLY ONE WHO SEES THE MASSIVE ORB OF PURE EVIL ABOVE US RIGHT NOW? AND HOW THE HELL DO YOU HAVE AN ANY IDEA WHAT THE FUCK IS GOING ON? I'M THE ONE WHOSE BEEN HAVING PROPHETIC, MATRIX-LIKE DREAMS!
In Oh God, Not again!Neville, out of all people, is the most sane character in the entire cast.
Shinji Ikari in Nobody Dies, who is basically a well-adjusted and sane version of his canon self. Everyone else is totally weird.
Even though Kyon and Chisame have had their backstories revised when they're brought into The Emiya Clan, they retain their personalities perfectly. Everyone else in the Clan is insane, weird, perverted, or otherwise, while these two struggle but usually succeed to keep their sanity amidst a household where random explosions, Eldritch Abominations, and harem antics are considered normal.
Going by Nasuverse stats, Kyon has EX rated Common Sense. Chisame has A+.
Andy from Calvin & Hobbes: The Series eventually became this after initially being The Generic Guy. He's usually the only one who can keep everyone in the group from arguing. Hobbes and Sherman also act like this, but have their own moments of insanity as well.
During the crossover "Calvin's Batman Adventure", the villains play this role to Calvin.
Fluttershy and Pinkie Pie in Twillight Sparkle's awesome adventure, in two very different ways. Fluttershy is the only character whose personality isn't completely warped and who doesn't worship the metaphorical ground Admiral Awesome treads on, as well as being the one most likely to come up with good plans (which are then ignored because the author doesn't like her). Pinkie Pie, meanwhile, is a Fourth Wall Observer in the story and therefore is the only one who realizes that the whole thing is just a terribly-written fanfic.
In The Wizard In The Shadows this alternates between Emrys, Boromir and Aragorn, though mostly Emrys and Boromir, both of whom regard most of the cast (particularly Harry) as batshit insane.