Some of the human Looney Tunes characters can be grouchy. For example: Yosemite Sam, Elmer Fudd, and some other minor characters like Casper Caveman.
Ratchet from Transformers Animated is justified in that he is a war hero who has seen enough to have lost his innocence about things and has become gruff to a fault. Even Captain Fanzone, the by-the-book police officer, has told Ratchet to work on his people skills.. Hilarity Ensues when Ratchet's attempts to bring a pregnant woman to the hospital in his ambulance mode make her leave and take a cab. His cynicism is often contrasted with Optimus Prime's idealism and patriotism.
When you've been mutilated by a part-stealing bounty hunter, seen the soldier you were supposed to protect mindwiped in front of you (hell, been the one to mindwipe her!), and the lobotomized body of your old war buddy is turned into a transport for some washout Elite Guard cadet, cranky makes sense.
Beast Boy's ex-teammates the Doom Patrol show up in the last season of Teen Titans, and start reminding BB that sometimes you have to Shoot the Dog to save the world. Then the kids after whom the show is actually named show them that all the Heroic Sacrifices they only thought were necessary can just be undone off-screen anyway.
Benson from Regular Show, especially when threatening to fire Mordecai, Rigby, or both.
To be fair, he has this behavior based on dealing with the two of them. He sometimes acts like this towards Muscle Man when he's being obnoxious, but he's actually fairly nice towards Pops, Skips and Thomas.
Twilight Sparkle from My Little Pony: Friendship Is Magic started out as a rare case of the Grumpy Bear being the main character, as well as the Only Sane Pony. Later on we get Cranky Doodle Donkey: it takes an entire episode of being harassed by Pinkie Pie and a reunion with a long-lost lover to make him crack a smile.
Dan from Dan Vs. fills the trope when things wrong him in the opening.
Huffer from Transformers Generation 1 was built for this role almost literally; fellow crank-case Gears might count as either this or a Sour Supporter, if A] he wasn't faking it for the sake of morale and B] he ever actually said anything in the cartoon.
Care Bears: Grumpy Bear might say, "Of course you got all the way to the bottom of the Western Animation section before anyone thought of me, even though my name's on the page." He's the most practical of the bears, and the local Mr. Fix-it (which, according to Share Bear in the 1985 movie, is because he never complains). He tends to have the role of Butt Monkey. Being so grumpy perhaps makes the writers feel less guilty about giving him so much trouble. In fact, the whole reson he was created was to teach children that it's ok to be grumpy sometimes (but it's silly to let grumpiness go too far).
Gordon the Big Engine from Thomas the Tank Engine. His arrogance seems to stem from his inability to tolerate everything around him. James even lampshades his grumpiness in the Season 5 episode A Better View For Gordon.
James: Why are you complaining all the time? Gordon: Because I'm a big blue engine and I know everything! I shall complain whenever I want!
Don't forget George the Steamroller.
Even Thomas himself gets really grumpy. Even in the Season 2 episode Thomas, Percy and the Coal.