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Naruto The Abridged Series has the Third Hokage, Gladas the Village Elder and Bob the Other Village Elder (who still can't be Hokage).
Yugi's grandpa in Yu-Gi-Oh! The Abridged Series. He frequently fantasies about dying as he hates his life so much, is increasingly senile and seems to find nothing in life enjoyable. Except of course, for his rendezvous with the poster of the Black Luster Soldier …
Anime and Manga
Genryusai Shigekuni Yamamoto from Bleach, a shinigami pushing at least several thousand years, who constantly complains about the younger generation of shinigami when he is forced into battle. Counteracted by the fact that he is a Badass Grandpa.
Everyone is a kid to him and even when he does fight he speaks to his opponents as though they're naughty children he has to punish.
Mr. Nebbercracker in Monster House is shown at first to be the basic "Stay off my lawn" old man who took any toy that came near his house. However later it is revealed that this is a cover for his true intentions of protecting kids from the wrath of Constance, his child-hating deceased wife who has possessed his house for 40-so years and eats anybody who comes too close to her. Basically anytime he yells "Stay off my lawn" it is not so much a threat as it is a warning. Ultimately the main characters set her spirit free by blowing up the house and he loses his crotchety behavior, happily giving back all the toys he confiscated to everyone in the neighborhood.
Carl Frederickson from Up. He's grumpy and crotchety because his beloved wife is dead, and because he feels overwhelming guilt from an unfulfilled promise he made to her.
"There, you see? I'm an ugly, horrible, grouchy, old man!"
The self portrait of the Painter from The Painting. He softens up some when he starts teaching the group how to paint.
Films — Live-Action
The movie Grumpy Old Men, featuring Jack Lemmon and Walter Matthau, which focuses on two such characters fighting amongst themselves over old-man stuff and ages-long grudges. It got a sequel, Grumpier Old Men.
Albert, Death's manservant in the Discworld books, doesn't approve of anything that's happened since his apparent death some two millennia ago, especially not the changes to Unseen University (he was the first Archchancellor). And since he hasn't aged since he entered Death's Domain, he was probably a grumpy old man then as well.
There was a Saturday Night Live character, played by Dana Carvey, who was actually called "Grumpy Old Man". Every time he appeared on the show, he would make a rant against modern-day society, starting off with his Catch Phrase ("I'm old and I'm not happy!"), contrasting how things were in his day. ("In my day we didn't have hair dryers! If you wanted to blow dry your hair you stood outside during a hurricane. Your hair was dry, but you had a sharp piece of wood driven clear through your skull! And that's the way it was and you liked it! You loved it! Whoopee, I'm a human head-kabob!")
"Life was a carnival! We entertained ourselves! We didn't need moooovin' pitchurrrres. In my day, there was only one show in town — it was called 'Stare at the sun!' ... That's right! You'd sit in the middle of an open field and stare up at the sun till your eyeballs burst into flames! And you thought, 'Oh, no! Maybe I shouldn't've stared directly into the burning sun with my eyes wide open.' But it was too late! Your head was on fire and people were roastin' chickens over it. ... And that's the way it was and we liked it!"
Adam Schiff and, to a lesser degree, Arthur Branch on Law & Order.
JAG: Basically, every Admiral/General or senior NCO on the show near retirement will exhibit these traits. It goes for those who have already retired too. It’s justified, since those characters are almost always involved to some extent in an investigation or trial.
The BBC series of one-off TV shows Grumpy Old X takes a bunch of Real Life grumpy old celebrities, and has them do talking heads about whatever the x is this time. The initial ones were Grumpy Old Men and Grumpy Old Women, more recently there have been things like Grumpy Old Holidays, Grumpy Old Christmas etc etc etc.
Captain Picard of Star Trek: The Next Generation started out as this, yelling at Wesley for coming onto his bridge. Becoming more of a Cool Old Guy when the series took off, though he still held onto some of the traits of grumpiness.
Peo Persson from Vintergatan, every installment — though he lightens up off-work, and with his wife. Of course, his wife is frequently kidnapped, so this isn't often. He has become less of this later, though, instead becoming more of a jaunty old man.
Andy Rooney on 60 Minutes embodies this trope so perfectly, it's usually pretty hard to take him seriously. Honestly, he probably knows how ridiculous some of his gripes are, but he also doesn't care.
The "Old Man" of Pawn Stars often reminiscences about the "good old days". Never seen even cracking a smile.
Doctor Who: The Doctor started off like this. Thanks to The Nth Doctor, he's since racked up several centuries while generally looking younger (coming full-circle in his Peter Capaldi incarnation). The Tenth Doctor explicitly compares his early personae to a kid "trying to be old and grumpy and important, like you do when you're young."
Inverted in Graduados. Andy is a rocker in his forties, who just found his long-lost son…and he's a bit upset because he's such a nice, correct and good guy.
Diana Trent in Waiting for God is practically a Most Triumphant Example. Over time we realize that she's like that because her youth was incredibly adventurous, daring, and exciting, so being incarcerated in a seedy old folks' home is a living hell for her.
Lampshaded and subverted by the Youtube-based anime-reviewer, Grumpy Jii-san (lit., 'grumpy grandpa'). Very rarely does he ever make some sort of complaint against something new, despite his name, and he has adapted to modern times quite well, going so far as to review anime that is being streamed on the internet. Jii-san also has some editing prowess: in his review of Irresponsible Captain Tylor, Jii-san spliced images of himself into the intro of the anime. Every now and then, he brings out some Laserdiscs, or references some old movies or artifacts.
Grumpy Jii-San *during his review of Baccano!*: "For that matter, does anyone even remember passenger trains?"
Grumpy Old Man Logan in this Marvel: What The?! vid.
Ed Crankshaft, originally from Funky Winkerbean then later spun off into his own strip, Crankshaft. He's not only a Grumpy Old Man, he's a school-bus driver, who keeps a running tally of how many times he's destroyed his neighbor George Keesterman's mailbox with the bus, and how far he can make parents or the kids chase the bus before they give up.
Funky himself seems to have (d)evolved into this, after Time Skip #2.
In one Dilbert strip, a scowling employee says that he had only plain zeros and ones to work with when he started programming, and sometimes not even ones.
Comedian Godfrey's own father qualified. What makes this funnier is that his father is Nigerian, and is acted with an appropriate accent. When l'il Godfrey complained about missing the bus, he talked about how he had to walk one hundred miles to school every day. When Godfrey had managed to save up $195 towards $200 Air Jordans and asked for a loan, his father talked about how, in their day, he did not have feet. He had to borrow his feet.
Billy Crystal used to do routines based on his own grandfather, talking about the Bad Old Days ("Happiness? What happiness? We were miserable, and we loved it, goddammit!"). Listening to the routine, it's clear that he based Miracle Max off of this character.
Long Beards in Warhammer. Their special ability allows units to reroll a morale test to prevent their grumpy leers and words of "told you so".
Jolee Bindo from Knights of the Old Republic is an interesting example, he purposefully acts like a stereotypical Grumpy Old Man because he finds humor in it and (jokingly?) thinks youth expects him to act like it.
In Jade Empire, another Bioware game, you can run into a pair of old men in Tien's Landing grumbling about the state of the town. Addressing one of them will get you moaned at, but the other will explain he means nothing by it, and they're just passing time.
Ezio Auditore has become this by the time Assassin's Creed: Embers takes place. He's 65, and just wants to enjoy what little time he has left with his family in peace, away from the Templars and the Assassins, which is why he doesn't take too kindly to Shao Jun pulling him back into it all. However, he does warm up, in typical Ezio fashion, once he gets to know her properly.
Huang Zhong from Dynasty Warriors, a Badass Grandpa at 62, defeating generals half his age. He also tends to make comments that have him come across less like a legendary Chinese hero and more like a cranky old man with a bow and arrows.
In LA Noire Finbarr "Rusty" Galloway and Hershel Biggs both fit this trope like a glove. Despite (or because of) his long history of service in the LAPD Rusty has become grumpy, ornery, and a borderline alcoholic who wants nothing more than to chalk each case up to a suicide and go home. Hershel Biggs is referred to as a basket case and an institution, and is explicitly partnered with disgraced protagonist Cole Phelps to spare the rejects from being partnered with anyone else on the Arson desk.
Tagon's dad in Schlock Mercenary, a retired general, is every inch of this. Directly referenced when a young intelligence-analyst sarcastically asks if he walked uphill both ways to get to school as a kid... and he replies that yes indeed, he did, due to living in an old space-habitat with a flaky artificial gravity generator that they had to cycle around noon.
Played with in the Futurama episode "A Clone of My Own". When Fry has to pretend to be the professor so the Planet Express crew can sneak into the Near-Death Star, but the robot guards are skeptical about his age, Fry instantly convinces them he is a 160-year-old man by shouting "Hey, you kids! Get off my lawn!"
One of Mike's personalities from Total Drama Revenge of the Island, Chester, is an old man who complains and talks about his youth, never mind the fact that Mike is a teen.
Grandpa: … and your Blu-Ray Discs and your pierced scrotums and your bull frogs and your telekinesis and your Marvel Comics and your YouTube.com and your nuclear physics and your ingrowing toenails and your Gears of War and your Quentin Tarantino and your power steering and your elevators and your six-person space capsules and your illegitimate offspring and your — hey, why did it fade to black? Am I dead? Yugi: No, Gramps. It's just the end of the trope. Grandpa: Oh, fiddlesticks!