Professor Farnsworth on Futurama takes this to the lengths of parody and beyond. Case in point:
"Even I laughed at me when I proposed the cross-species genetic analyzer, but I guess I showed myself!"
"Everyone's always in favour of saving Hitler's brain. But when you put it in the body of a great white shark, ooh, suddenly you've gone too far!"
He builds Doomsday Devices a lot. Oh, he doesn't plan to use them, he just seems to think they're cool. "I suppose I could part with one and still be feared..."
At one point the Planet Express crew were figuring how to enter New New York's Central Bureaucracy.
Prof. Farnsworth: You can't just waltz into the Central Bureaucracy! It's a tangled web of red tape and regulations. I've never been, but a friend of mine went completely mad trying to find the washroom there. Leela: Then we'll need a guide, someone who's been there before. Prof. Farnsworth: Oh, I've been there. Lots of times! (Laughs maniacally)
One episode revealed that he spent twenty-five years in a mental institution starting when he was a teenager.
His rival and former student, Professor WERNSTROM! is of the evil (or at least asshole) variation.
Professor Frink of The Simpsons is a rather more amicable Mad Scientist, always apologetic when things go wrong with his inventions, and a passion for inventing crazy things like self-aware robots that only scrub floors, auto-diallers with retractable wheels, automatic tap-dancing shoes, buildings that can sprout legs and run away from danger, and hamburger earmuffs.
Frink:(as a radio controlled baby-plane with his son in it crashes) Oh dear. My wife is going to kill me.
The Brain of Pinky and the Brain always devises a scheme to take over the world, several of them involving machines and potions. He quite often pilots mechanical bodies to appear human and once tried to hypnotize everyone by feeding them pancakes laced with hypnotic fluid.
The original 1993 series has Dr. Karbunkle, who often creates inventions for Limburger and his minions to use against the Biker Mice and also experimented on the Biker Mice, which resulted in Modo getting an eyepatch and a robotic arm and Throttle being blinded and needing special sunglasses to see.
The 2006 Sequel Series has Dr. Catorkian, a Catatonian scientist who creates inventions to help the Catatonians and Ronaldo Rump defeat the Biker Mice.
An interesting example occurs in Adventure Time. Princess Bubblegum is the sweet, benevolent ruler of the Candy Kingdom, but is also a highly intelligent scientist. Although normally level-headed and innocently sweet, she has created two zombie plagues, created a giant immortal candy sphinx who almost destroyed the kingdom, created a screaming nutcase who threatened her with his own sword, has skeletons chained to her walls, created a potion that can permanently paralyze someone, killed a jellyfish to make a sandwich, tried to have the Duke of Nuts killed, and tortured the Ice King. Her "For SCIENCE!" attitude, and her devotion to the law, cause... interesting things to happen.
It's all but stated that her insanity is the result of brain damage from the accident that scarred her. It's a pity that the only character in the show who had healing powers (Gaia, that is) was the one Blight would never be willing to go to for help. Just remember the times when she tried to kill or at least harm the Spirit of Earth.
Megavolt from Darkwing Duck. Likewise Bushroot, who's usually ignored in this capacity, because his "mad science" is botany.
Dr. Sevarius from Gargoyles isn't quite mad so much as he is amoral, but he displays a touch of the theatricality that is the hallmark of the best nutty professors.
Then again, he is being portrayed by Tim Curry. Go figure.
Dr. Cinnamon J. Scudworth of Clone High certainly qualifies, even though his day job is as a high school principal.
The Dark Knight always seemed to be neck-deep in mad scientists on Batman: The Animated Series. Within the first five episodes of the show, he runs afoul of Man-Bat, the Scarecrow, and Poison Ivy, scientists-turned-supercriminals all. Scarecrow actually goes the whole hog with the trope, as his initial appearance features a plot to ruin the university he was fired from and murder all those who called his sanity into question.
Yes, killing them all will show that you are PERFECTLY sane...
Hey, it's not like they'll be saying otherwise.
Indeed, it should settle the question of his sanity quite comprehensively.
Joker:Beneath this puckish exterior lies the mind of a genius years ahead of my time. In the weeks young Robin was under my tutelage, I used him as the subject of my greatest experiment. Using cutting-edge genetics technology which I pinched here and there, I encoded my DNA in a microchip and set it in Bird Boy's birdbrain.
Johnny Test's older sisters Susan and Mary are both Mad Scientist teenagers. Also their friendly enemy, Eugene, a.k.a. "Bling Bling Boy".
The character Vendetta on the show Making Fiends is a mad scientist, as she creates tons of fiends, which also can be considered as forms of life.
The title character of Invader Zim is a mad scientist himself. In fact, in a script for an incomplete Start of Darkness episode about him, Zim was actually a military scientist for his race whose creation, an "Infinite Absorbing Blob" was responsible for killing two of his previous leaders.
Dib and Professor Membrane would arguably qualify as Mad Scientists. Dib perhaps more so since his inventions revolve around his all-consuming obsession to destroy ZIM, whereas his father's inventions are more geared toward helping humanity. Even the Super Toast.
Wheeljack of Transformers Generation 1 is one. Part of his appeal was him convincing the other Autobots that his crackpot inventions were worth something.
His Shattered Glass counterpart is also a mad scientist, but less the cheery genial type normal Wheeljack is, and much, much more pure distilled ranting They Called Me Mad! type of mad scientist.
Dr. Arkeville from the G1 cartoon. Though his madness was one upped by Starscream himself in Countdown to Extinction.
Tarantulus of Transformers: Beast Wars is, if not a mad inventor, certainly crazy enough and scientific enough and treacherous enough to qualify for Mad Scientist.
This is actually a case of Character Development; in the first season, while he was the Predacon Science Officer, he was characterized more as "that creepy bot who'll eat anything he can catch". This was Adaptation Displacement—in the original toylines, he was a (still cannibalistic) ninja warrior.
Transformers Animated has Prometheus Black. He started out messing around with biochemical enhancements to try and beat out Professor Sumdac's robotics industry, but after a lab accident changed him into the supervillain Meltdown he went into full vengeful mad science mode. The chemical warfare specialist Oil Slick might also count, although outside the fact that he's a ninja who developed the Transformer equivalent of ebola not much is known about him.
Animated! Blackarachnia also has elements of this. The Allspark Almanac reveals she invented triple-changing, and her attempts to better understand her techno-organic mutation lead her to try and create another hybrid...resulting in Waspinator.
Dr. Thadeus "Rusty" Venture on The Venture Bros., although his lack of ambitions and laziness mean that he comes up with far fewer superweapons and far more get-rich-quick schemes than most of his ilk. Other M.S.'s in the Ventureverse include Pete White and Master Billy Quizboy, Jonas Venture Jr., Otaku Senzuri from the lost pilot, Professor Impossible, Mike Sorayama, Dr. Septapus, Baron Ünderbheit (implied), and Phantom Limb (implied confirmed, as part of his backstory)
The Tick has several: Brain Child, Professor Chromedome, mostly non-evil Julius Pendecker, and, a more benevolent (though unnerving) version, Dr. Mung-Mung, whose best-known creation is a super-strong giant made entirely of tongue.
Heloise from Jimmy Two-Shoes is this. Despite being a small, petite girl, she is very intelligent and sadistic as she makes inventions for Misery Inc. that would spread misery to her town and also likes to destroy things for fun. She does have a soft side though as she has feelings for Jimmy buts treats everyone else with disrespect, even her own boss.
You might even count Professor Utonium, although he's far more benign than most. Every time he creates something useful (including the Girls themselves), it's by accident. But when he tries to do something intentionally, it leads to a disaster.
Also Cesar. He single-handedly invents weaponry that can take down an entire highly-trained government base, but is a Cloud Cuckoo Lander on a good day and a totally lacks any sense of practicality or ethics on a bad day.
Franz Hopper from Code Lyoko is less "mad" than he is "slightly unhinged". Still, though, he manages to create a computer program that can venture into the world, take people hostage, create poisonous gas, create blizzards, and many many other things, so he definitely counts.
Simon Bar Sinister, the main antagonist on Underdog, a short, nasty-looking scientist only about two feet tall, who's goal was to Take Over the World. Unlike most examples of this trope, he tended to actually listen when his henchman Cad Lackey made suggestions.
The first Superman short, "The Mad Scientist," has one as the villain, threatening to enact vengeance on all those who laughed at him with his electrothanasia-ray.
Wallace from Wallace & Gromit is an eccentric, absent-minded inventor, although he usually uses his inventions for mundane things such as window-washing and humanely rounding up bunnies so they don't get in the way of the town's upcoming vegetable-growing competition. This has resulting in one case of mind-switching, Wallace turning into a Were-Rabbit, a penguin attempting to use his inventions for a jewel heist, and Wallace nearly getting killed several times. Luckily, his dog Gromit is loyal to a fault, an acepilot, and smart enough to be able to fix things whenever they go wrong (and they do, frequently).
Professor Crazyhair from Yakkity Yak is a fairly benign and friendly example, but is still mad.
The Alvin Show has Clyde Crashcup, who tries (but always fails) to "invent" something.
Grojband has Kin, as he's often the most morally dubious of the band given his creepy obsession with science.
Rick Sanchez from Rick and Morty is as mad as they come, though he replaces the usual creepiness and cackle-happy lunacy with heaps and heaps of apathy for everything and everyone else (except maybe his grandchildren Morty and Summer). He's someone who gives absolutely zero fucks about leaving his entire dimension to die, and fleeing into another where his counterpart had died half a minute ago, burying him on the back yard and taking over his life, and that makes him just as crazy as the cackling lunatic the trope usually conjures.
Professor Weirdo and Count Kook are creating a monster with six drops of essence of terror and five drops of sinister sauce. Professor Weirdo means to add a tincture of tenderness so the creation would not turn on him, but Count Kook accidentally knocks in the entire beaker. The creation becomes the childlike Milton The Monster.