The goblins in "The Silent King" most definitely count as this, particularly Gummy.
The Royal Tart Toter. That poor, poor man. Although he's actually pretty damn happy and upbeat, he's completely insane, blind, and deaf. He's still completely dedicated to his job of delivering the royal tarts, even though he's in no condition to, and he's in a mental hospital.
Baby-Snaps. As a child, he was in an orphanage. When Princess Bubblegum showed up to cheer up the kids, she asked Baby-Snaps what he wanted to be. He said cheerfully, "I want to be a princess like you!" Princess Bubblegum giggled, thus starting Baby-Snaps's Start of Darkness and Sanity Slippage. Baby-Snaps went crazy and started taking hostages in the kingdom in order to get Princess Bubblegum's crown. He was later chased by guards, and he blissfully fell off a cliff to avoid being captured. He survived, and ended up in a mental hospital, where he was crowned "Princess of the Grass Kingdom."
Princess Monster Wife. She was created by the Ice King from the stolen body parts of his favorite princess. The princess was hideously deformed, but a genuinely sweet, damaged character who needed a hug. Although the Ice King constantly told her she was beautiful and wonderful, Finn and Jake and the penguins were continuously repulsed by her appearance. She spent most of the episode crying and questioning her own existence, and she eventually killed herself for the good of the other princesses, by returning their body parts to the rightful owners. It is implied her spirit lives on, though.
Prince Huge. He had been transformed into a giant, hideous frog, and the only way to break the spell was with a kiss. So he went around kissing everyone, trying to break the curse. Everyone he encountered assumed he was trying to eat them, and he garnered a reputation for being an evil monster. After learning of his backstory, it's impossible to NOT feel for the guy. His story had a happy ending, though- Finn turned him back into his normal form, and all is well.
To a lesser extent, the squirrel from "Up A Tree" qualifies. He admits that the other animals who live in the tree pick on him for wanting to be a flying squirrel. During his conversation with Finn in the jail cell, it's hard not to feel sorry for him.
The Magi creature from "Little Dude" qualifies. He hid himself underground so he wouldn't accidentally curse anyone. It's revealed the poor guy had an abusive father who kept calling him a bad wizard.
The Lemon Children. They all almost starved to death. One of their brothers is dead. Their dads are the Lemongrabs, and the one who actually loves them is tortured by the other one. Poor little things.
Lemongrab 2 is seen by a large portion of the fanbase as a woobie, especially after "Too Old" where he was horribly disfigured and in very bad shape, as well as being horribly abused by his older brother before finally being eaten whole by him while making a passionate speech to his children.
Johnnie from "Bad Timing". He was picked on by Lumpy Space Princess when he was in high school (she called him "Ugly Johnnie") despite this he still goes out with her and it seems like they would be a really good match until she goes bat-shit crazy and accidentally traps him in an alternate dimension out of jealousy.
Flame Princess in "Earth And Water". Especially after we learn that part of the reason she was locked up for most of her life was because Flame King thought she would usurp his throne. He was so afraid of this happening that shortly after she was born, he had her thrown out into the woods to die.
She is also betrayed and one point and her father promises to marry her off in exchange for helping to overthrow her, because (as they acknowledge) the Flame Kingdom is super Shakespearean.
Shoko from "The Vault". If her past is to believed, her parents sold one of her arms for a computer, and then abandoned her at a dojo. Then, she's forced to steal from Princess Bubblegum, who is probably her one and only friend, and ends up falling into a radioactive river, mutating into a horrible monster before curling up under a tree to die. And to top it off, her spirit remains restless for possibly thousands of years until she's able to return the amulet she stole from PB by acting through Finn's subconscious.
Marceline has gone through some crazy tragic times. First she survives the Mushroom War, and presumably lost her mother as she had to be cared for by Simon in the "wreckage of the world" who is going insane right before her eyes. She also gets turned into a vampire against her will, which kind of forced to remain (as she puts it) "a messed up kid". Then she clearly has a strained relationship with her father, a terrible relationship with her Jerkass boyfriend Ash, a strained relationship with Princess Bubblegum (that they are overcoming), and has to know that many of the people she loves like Finn and Jake will grow old and die before her eyes.
Even Finn, considering all the things that happen to him, from getting beaten up all the time, to losing romances, and of course possibly the only human remaining, yet he still keeps an unbreakable happiness. Up until season five anyway, and season six's Breezy is a PG-rated version of depression.
Fern, by all account. He's basically Finn, and he's a version of Finn that succumbed to his depression. As a paradox clone of Finn, he's got every single memory Finn had until the point he was created, but he has to live as a self-deprecating grass clone that no one will ever recognize as the original. He can't eat, he can't enjoy anything he did enjoy as Finn, and he has to see Princess Bubblegum, Jake and everyone he knew rooting for Finn, a better version of him who gets to live "his" life. Eventually he snaps, and he tries to get back "his" life by getting Finn's place, just to end up as a bucket of still living freshly cut grass. Gumbald offers him a new lease at life, and he ends up as the Green Knight, a deformed warrior, little more than hired muscle for the new Big Bad. Eventually, he makes amends with Finn and frees himself from the grass demon just to known he's going to die soon because the Grass Demon provided him with a body. He dies, with his last breath asking to be brought to the Tree Fort...that was just destroyed. He barely gets his final wish, as his body turns into a seed, and the seed into a Sacred Tree holding the now restored Finn Sword for Shermy to safekeep.
