In Animal Land, llamas being plucky comedy reliefs seems to be their entire species schtick.
Sasha "Potato Girl" Brauss of Attack on Titan. In a series set in a near hopeless war against towering, man eating monsters, she's the resident goofball, with an appetite about as big as the Colossal Titan.
Connie runs a close second behind her, and is often paired with Sasha for comic moments. In a series where named characters die in handfuls every arc, they were also planned to be killed as the series progressed, but were spared by their popularity and editor warnings.
Hanji Zoe, considering how she is an eccentric Mad Scientist and has an unhealthy appreciation for Titans. But as the series continues, we are reminded just why she is a Squad Leader and senior officer in the Survey Corps.
However, after getting dangerous they all lose this as their primary characteristic. Especially Hange.
Code Geass features a Britannia comic relief, Rivalz Cardemonde and a Japanese comic relief, Shinichiro Tamaki. Lelouch can confirm that. He's been around both of 'em. Rivalz' friend Lelouch Lamperouge by day, Tamaki's idol, Zero by night.
Saito of the Japanese police. He's kind of like Matsuda in that he's a member of a special taskforce with a tendency toward humorous bumbling (Saito has twice been shown using his own name when undercover), and his unrequited crush on Kirihara is played for laughs. He's also something of a Crouching Moron, Hidden Badass, which makes sense, as he's a muggle who has regularly been up against super-powered sociopaths and has survived.
Misa Amane. Indeed she and Matsuda were the only characters who used most of the "sillier" anime tropes, like puffy cheeks, Face Faults and, at one point, repeatedly hitting Light on the chest with Looney Toons sound effects).
Ryuk. He makes off-hand humorous comments that usually involve apples even during the most serious scenes, and almost always chuckles loudly at any new plot or character development that occurs.
Dragon Ball: Because of the light-hearted and humorous nature of the show, especially since it started as a gag series, every character, including many of the villains, have funny moments.
Krillin is given this role in pretty much every Dragon Ball Z Movie he is in, the most famous case of him playing this role was in the Super Android 13 movie where he was beaten up by Chi-Chi, clonked his head twice, had hot coffee spilled on his head, had his face fried by a stray energy bolt, had a large pile of snow dumped on him, had Vegeta sent flying into him, slipped and skidded past the main villain when he was about to attack him and was humiliated in the hospital.
Mr. Satan/Hercule is mostly treated as a joke, and his main purpose is to act like a grandiose idiot, get beaten up by villains, and be the Fake Ultimate Hero. However, he does prove to be useful on several occasions thanks to, essentially, being very good at PR. Despite being comic relief who wouldn't last five seconds in any major fight, he's notable for both managing to contribute to saving the universe from Majin Buu and being the only character to survive the entirety of Dragon Ball Z without dying once.
Battle Tendency: The Jojo of this part, Joseph Joestar himself also works as the comic relief, showing a lot of hot-headed and careless behavior that leads him to awkward situations such as when he playfully greeted an immortal who just slaughtered a bunch of Nazis.
Stardust Crusaders: Several, the already mentioned Joseph Joestar getting in awkward situations. Jean Pierre Polnareff, a Frenchman who has bathroom problems and more than once finds himself in a life or death situation that involves a toilet. Also, Hol Horse, a servant of Dio who pursues the party. At first serious business, later comic relief.
Diamond is Unbreakable / Diamond is not Crash: Okuyasu Nijimura is a school delinquent that claims not to be a smart person, and demonstrates it numerous times.
Vento Aureo: Narancia Ghirga who, despite being two years older than the main character, displays a very childish behavior that matches his appearance. Also Guido Mista when the number 4 is involved.
Stone Ocean: Foo Fighters, being a bunch of plankton taking the form of a girl, thinks that prison is a fun place. Narciso Annasui who later becomes the main comic relief as being madly in love with Jolyne, he is not afraid to express it in front of her despite her general disinterest or obliviousness.
Steel Ball Run: The deuteragonist Gyro Zeppeli, when he's not busy being the serious cool guy spends his time planning bad jokes and songs that Johnny really finds clever.
Shiho from Mai-Otome. Though some of her antics are usually the cause of (or contribute to) the problem of the day in early episodes, she becomes surprisingly effective near the end, while retaining her goofy madness.
Shiho being this is rather odd, as her original Mai-HiME incarnation was a serious, plot-relevant, and much darker character, with little-to-no comedic moments.
Boss and the remainder of The Team Normal also were Plucky Comic Relief characters. Boss even lampshaded is in one Great Mazinger, wondering why he must be the Plucky Comic Relief.
In Mobile Suit Gundam 00, this is Patrick Colasour's primary role. Every battle he's in, he gets shot down, usually by a Gundam, yet unlike most other characters, he survives every time, earning him the nickname "The Immortal Colasour". And he's considered the best pilot in Europe!
He's also loyal to a fault, as shown when the UN-Armed Forces abandons him in the middle of the Taklamakan Desert after his AEU Enact was shot down and everyone assumed he was dead. He still returned to the base as if nothing had happened a few days later.
Minoru Mineta from My Hero Academia is literally a Plucky Comic Relief, as in, his powers revolve around plucking sticky berries from his hair.
Kaminari Denki and Mina Ashido tend to get the most spotlight during lighthearted situations, as theirpersonalities are often used to lift up the spirits of the group.
Naoki from NANA fits this trope particularly well: Despite all the drama that goes on in the series, he is oddly immune to it and (in present time) seemingly oblivious. The writer herself admits that he was written to round out the two rival bands in the story — in essence, he's a throwaway character with no real backstory — but he usually ends up being used as Mr. Exposition in side stories.
Uzura in Princess Tutu spends much of the second season filling this role, although she has a few plot-important moments towards the end and is never quite able to stay completely detached from the action.
Sailor Chibi Moon in the Sailor Moon anime. Her Pink Sugar Heart Attack rarely worked, and it was pathetically weak. This is in contrast to the manga where it actually does work well on a regular basis.
Shaman King gives us Chocolove, who pretty much tries to invoke this because he wants to be a comedian. Ironically, his humor comes from the fact that his jokes aren't funny. He's also fairly useful, unlike some other examples.
In the last episode of Slayers NEXT, Lina concludes that the only reason Martina survived the confrontation with the Big Bad was because she is the Plucky Comic Relief character.
Tokyo Ghoul has several, all of which become serious once the tragic final arc begins.
Enji Koma, the goofy-looking head waiter of Anteiku. He's primarily there as a Butt-Monkey, getting no respect from his peers as he waxes nostalgic about his glory days. He comes out of retirement, proving to be a Death Seeker out to atone for his bloody past. It is left unclear whether or not he died during the last stand at V14.
Seidou Takizawa, the easily-excited and jealous junior Investigator. He spends most of the series getting picked on, embarrassing himself while drunk, or otherwise being the Butt-Monkey around the office. He has up performing a Heroic Sacrifice, and is presumed dead after being maimed by Noro. The sequel, however, reveals him to have survived as a deranged Half-Ghoul.