Unflappable Guardian

They always present a polite and kind face, quietly protecting their charges. Can appear dense to others, but these are intelligent characters who note details and quirks and file them away without letting others know they're doing it. They would prefer having the mysterious stranger who showed up in the first episode come live with you, just to find out their real intentions. Or they'll casually suggest you go visit that abandoned field where a ghost is supposed to haunt.

Keeping the peace and serenity of the group and household is what prevents them from outwardly doing things, since they seem the type who could be very dangerous and create chaos if they wanted to. Anyone pointing this out (usually a villain or very smart character) will be met with a pleasant and suspicious dismissal.

Very commonly a character's mother or grandparent, this often overlaps with the Harem Nanny, and sometimes, as a bonus, she's a Hot Mom.

Compare the Standard Fifties Father, who is also unflappable but in a different way. Contrast Resentful Guardian.

This page could use more examples from media other than Anime and Manga.

Anime and Manga

 * Kasumi Tendou of Ranma ½ is one of the earlier manga examples of the trope: She's arguably the only member of the cast (regular or extended) who doesn't have some sort of major mental issue (or three).
 * Although some argue that Kasumi's utter inflappability simply and indestructible cheerfulness mask deeper issues.
 * Sanae in Happy World is immediately but quietly suspicious of her nephew's sudden Magical Girlfriend. She also puts down (violently) the perverted advances of her daughter towards other characters.
 * Katsuhiko/Yosho in Tenchi Muyo!
 * Shigure in Fruits Basket is a skilled, albeit always well-intended, manipulator who uses Obfuscating Stupidity to his advantage.
 * Aunt Haruka from Love Hina. Though unflappable in the anime, the manga shows her making a quick and uncharacteristic exit from Kanako, and a full-blown loss of temper at Seta.
 * Tomokazu's cousin Nanase in Yumeria.
 * Akiko in Kanon.
 * Maria from Hayate the Combat Butler is a Hot Shounen Maid.
 * Watari of Death Note.
 * God, the dorm leader in Maria Holic. She holds an iron grip over the dormitories, and occasionally shows mercy towards her students, but is definitely smarter than she lets on. Everything is accounted for.
 * Kisuke Urahara from Bleach.
 * Mr. Deerfield, Christine's all-purpose butler, from Daa! Daa! Daa!. He is the one containing Evil Chris when her fits get out of hand, serving as a reverse Berserk Button.
 * Isabella from Paradise Kiss.
 * Miya Asama, the Team Mom in Sekirei. Though she maintains a cool Yamato Nadeshiko charm, sekirei familiar with her are terrified of her power, and she can make herself understood without losing her arete.
 * Mikael from Tenshi ni Narumon fits this trope to a T, mostly in regard to Noelle.
 * Raphael, on the other hand, while may not look like it at first glance, is this trope (albeit well-intended) to Mikael.

Live-Action TV

 * The Beverly Hillbillies: The family's patriarch Jed Clampett never let anything worry him, and (almost) always had the right advice to give Jethro and Elly May. His advice might not have been culturally appropriate, but it usually worked out well when it was followed.