Happy shows need sad characters to balance the emotionality and the realness of said world. It is a simple mirroring of society, where life is never fully happy, dotting everyone with moments of sadness, grief, and depression. The sad times make happy times ever happier, and they often work as teaching lessons and moments of growth.
Sad characters are also a source of humor and entertainment on TV. Humanity copes with its sadness through humor, and audiences often cope with their life's disappointments, failures, loneliness, and depression through sad screen characters. As with everything, variety is the spice of life, and so it goes for sad characters in overall chipper series.
Teddy (Bob's Burgers)
The lonely, middle-aged regular at Bob's Burgers, Teddy doesn't start off as Bob's best friend. Linda's penchant for craziness, and her joie de vivre, paired with Bob's patience for craziness, and his accepting nature, was a safe haven for Teddy in a world not made for people like him. Teddy is uncool, overfriendly, unrefined, and simple.
In a world where Jimmy Pestos achieve more with faux bravado, Teddy is often rejected by most people. Bob's calm acceptance of a man who wishes he could have Bob's family life brings a ray of hope and joy to an otherwise sad character.
Bill Dauterive (King Of The Hill)
Bill started off as the coolest member of the gang. The muscular football player with a full head of hair, and a promising career in the army, Bill could not run away from his past. A childhood filled with emotional abuse from his father led him to marry an emotionally abusive woman. His marriage soon dissolved after years of his wife being unfaithful, and Bill became paralyzed by his trauma, unable to heal from a lifetime of abuse.
He has suffered many depressive episodes, but is lucky enough to have three best friends who want the best for him, including Dale, a man who loves Bill so much, he would "shoot his friend to prevent him from committing suicide".
Eeyore (Winnie The Pooh)
Eeyore is characterized by his grey coat, his droopy face, and his sad demeanor. A clear contrast with other happy characters like the overexcited, bouncy Tigger, and the jovial best friends, Piglet and Pooh, Eeyore has slowly become an icon for depression and its effects on people.
Battling the effects of his mental state, the depressed donkey speaks in a very monotonous drawl and moves very slowly too. Despite his depression, Eeyore's friends love him as he is, and accept him with as much patience as they accept the overhyped, unnecessarily bouncy Tigger.
Al Tuttle (American Dad)
Al Tuttle is Stan Smith's loner neighbor, who struggles for connection with those around him. In one episode, it is revealed that Al became incredibly obese, becoming a shut-in in his own home. When Steve and his crew clean his home for him for a fee, Snot becomes trapped under Al's butt, breathing in his butt air.
In another episode, Al achieves fame abroad thanks to the hidden camera in his home recording his sad life, like when he ate a whole cake thrown in a dumpster because he was feeling particularly vulnerable.
Featuring Ludacris (Big Mouth)
Big Mouth asks the question, "What would happen if pets were self-aware?" The answer is a self-aware, intelligent dog whose self-consciousness causes him to be depressed. Featuring Ludacris ponders deep philosophical questions about the meaning of life. His knowledge, however, causes him to be depressed, proving the adage that with great knowledge comes great sadness.
While other characters on Big Mouth often have their moments of happiness, Featuring Ludacris has no freedom, trapped in his home, unable to escape, and deeply saddened by his dependency on his family, and the loss of his agency as an intelligent being.
Gunther (Friends)
The cast of Friends is a happy-go-lucky bunch of 20 somethings living in New York. They hang around the coffee shop, Central Perk, drinking coffee, and talking about their relationships, sex life, and their careers. Unbreakable Kimmy Schmidt satirizes the show by renaming it, Six White Complainers, in a satire about how a group of people with great lives still manage to complain about trivial matters.
Like the cast member, Gunther, a side character, brings a lot of his own unhappiness to the show. He pines after Rachel who, at best, shows disdain and indifference towards him. Rather than live a great, full life, he lets his obsession with Rachel keep him in a perpetual state of longing and sadness.
Paula Small (Home Movies)
Paula Small is a divorced mother of two young children whose husband left her for a model in her twenties in Home Movies. Struggling financially while her ex-husband spends lavishly on his new trophy wife, Paula Small is disillusioned and lives her life in a constant state of nonchalance. This attitude affects nearly every aspect of her life, including her role as a mother.
She is very lax with Brendon, even when he gets into big trouble at school, considering Brendon more of her friend than her son. In an episode where she finds a new Italian love, Paula is revved up from her broken-hearted stupor. However, this doesn't last long when she finds out he was just using her.
Judith (3rd Rock From The Sun)
Judith is a "strident, power-mad tart", according to an insensitive Dick Solomon. A kooky show about aliens trying to blend in on Earth, 3rd Rock From The Sun is a very happy show about the crazy exploits of the Solomon family. At Dick Solomon's workplace, however, Judith is a fellow professor.
It is implied that Judith is a lesbian (or a bisexual) who has not been able to come out yet, resulting in her unhappiness and her lack of a love life. It is also hinted that she might be a misandrist who deliberately chose not to date despite showing an attraction to men.
Spike (Tom And Jerry)
Tom And Jerry is a simple show about a cat who loves to chase a mouse, and a mouse who loves to torture a cat. The classic cartoon frenemies have been popular ever since its first release in 1940. Another very happy show, Tom And Jerry still deals with dark issues, like a suicidal duckling trying to get eaten by Tom, or a dog who has had his freedom abruptly snatched.
Spike, another classic Tom And Jerry character, often suffers terrible things on the show to move the plot along. This happens, for example, when he is tied up to his dog house, his freedom stolen from him, and unable to beat Tom up. In many episodes, he suffers a severe concern for his son, Tyke, whom he loves dearly.
Squidward (SpongeBob SquarePants)
Squidward suffers the fate of the failed artist whose unrecognized talent leads them to a life of drudgery and mediocrity. The arrogant squid is unable to come to terms with the fact that he is just not a good artist or musician.
As a result, he is often depressed and angry, using a superiority complex as a defense mechanism against his lack of talent. To make matters worse. Squidward works for a cheap boss who detests workers' rights, and regularly finds creative ways to plunge his employees into slave labor.