In Terry Pratchett's Discworld books, the Alchemists' Guild are also Magitek mad scientists. Inverted with the character of Jeremy Clockson, who has the detachment from reality and dangerous obsession of the typical Mad Scientist because (most of the time, and in a very specialised way) he's saner than normal people.
The Igors of the Discworld series. Though typically the assistants of a Mad Scientist, they're known to conduct their own experiments, such as growing noses with feet, and their own special version of "self improvement". Though to be fair, the Igors in general are remarkably Genre Savvy — they know their place in the chain, and how to react when that chain is shaken. In fact, the clan foists off the most "modern" variant of their clan upon the Night Watch in an attempt to cease the corruption: that is to say, Mr. "Noses with Feet". Similarly, in Carpe Jugulum, an Igor working for vampires revolts at their innovations and revives the old master — not so much reviving the Good Old Ways as the Moderately Less Odious Old Ways.
Bergholt Stuttley "Bloody Stupid" Johnson may qualify, aside from his architectural and landscaping mishaps he made a mail-sorter with a wheel that has pi as exactly 3, it started churning out mail from the future and alternate universes until the post master smashed it.
Leonard of Quirm isn't so much mad as unable to foresee the consequences of his inventions.
While the Mad Scientist might seem quintessentially modern, he's probably Older Than Steam. The inspiration for both Mary Shelley's novel Frankenstein and the adaptations which distorted Frankenstein into a Mad Scientist came from a much older literary and popular tradition about Mad Alchemists, and their blasphemous, yet entertaining, obsessions with the creation of homunculi and the secrets of eternal life. The most well-known remnant of the old "Mad Alchemist" trope today is the Faust myth, and its literary adaptations in Marlowe's Doctor Faustus and Goethe's Faust.
An interesting fact is that the 1910 silent film Frankenstein features a scene of monster's creation that is highly relevant to an alchemical procedure of palingenesis (re-formation of a once-living organism from its ashes or from its severed parts by heating). No other film adaptation involves this trace.
Victor Frankenstein, as originally conceived in Mary Shelley's novel, was not quite a Mad Scientist. Although he sees himself as a descendant of Mad Alchemists, Shelley makes his character more rounded and his mental instability more subtly portrayed. However, within decades wildly popular nineteenth-century melodrama theatre adaptations recast him as a cackling Mad Alchemist.
While he's not a Mad Scientist throughout the novel, he certainly is one when he's actually working on bringing his creature to life:
My cheek had grown pale with study, and my person had become emaciated with confinement. Sometimes, on the very brink of certainty, I failed; yet still I clung to the hope which the next day or the next hour might realize. One secret which I alone possessed was the hope to which I had dedicated myself; and the moon gazed on my midnight labors, while, with unrelaxed and breathless eagerness, I pursued nature to her hiding-places. Who shall conceive the horrors of my secret toil as I sabbled among the unhallowed damps of the grave or tortured the living animal to animate the lifeless clay? My limbs now tremble, and my eyes swim with the remembrance; but then a resistless, and almost frantic impulse, urged me forward; I seemed to have lost all soul or sensation but for this one pursuit. It was indeed but a passing trance, that only made me feel with renewed acuteness so soon as, the unnatural stimulus ceasing to operate, I had returned to my old habits. I collected bones from charnel-houses and disturbed, with profane fingers, the tremendous secrets of the human frame. In a solitary chamber, or rather cell, at the top of the house, and separated from all the other apartments by a gallery and staircase, I kept my workshop of filthy creation: my eyeballs were starting from their sockets in attending to the details of my employment. The dissecting room and the slaughter-house furnished many of my materials; and often did my human nature turn with loathing from my occupation, whilst, still urged on by an eagerness which perpetually increased, I brought my work near to a conclusion.
The stories From Beyond, like At the Mountains of Madness, The Dreams in the Witch House and The Shadow Out of Time. While all of the above feature scientists, only the one in From Beyond is a genuine Mad Scientist. Though some of the others Go Mad from the Revelation, they never adapt Mad Scientist mannerisms, instead getting more realistic nervous breakdowns.
Herbert West, mentioned above in the Film of the Book (albeit updated to later in the 20th Century.)
Arthur Machen's The Inmost Light written in 1894 contains a rather horrific version of this trope.
There's one in The Great God Pan. While the novel seems desperate to make him slightly sympathetic, at least to a modern reader he comes off as a monster. Yeah, practice some experimental brain surgery with a teenaged girl completely infatuated with you, and clearly incapable of truly informed consent. What could go wrong?
The villain of Hilari Bell's The Last Knight is a rare example of a mad scientist in a fantasy setting, performing dubiously ethical experiments in order to give magical powers to humans (as, in the story's universe, only plants and animals have magic).
The Star Wars Expanded Universe introduce Qwi Xux, an incredibly brilliant scientist who designed the laser for the Death Star, the World Destroyers, the Sun Crusher and a number of other dangerous creations. Unlike many others in this trope her extremely guarded upbringing (she was raised by Imperials in an oppressive cram school where the price for failure was your hometown being obliterated) has caused her to develop a very naive and innocent view of her creations, having been led to believe they were intended for industrial applications (the Death Star would blow up a massive asteroid which the World Destroyers would then be able to harvest for materials, etc.).
Subverted to some extent in the George R.R. Martin-edited Wild Cards books. There are Mad Scientists a plenty, on both hero and villain sides. Or at least folks who have been infected with the wild card virus who are now determined to build androids, giant mecha suits and all manner of mad-sciencey devices. The kicker is that the inventions they create really are just piles of unworkable junk, and the particular power they have developed is the ability to make their crazy inventions work. Any attempt to analyze and reproduce the devices prove to be fruitless and show that there is no way they should function in the first place.
Professor Drummond from the Nick Carter short story "Nick Carter and the Professor" from 1902. This story appeared in the reprint anthology Nick Carter, Detective published in 1963 by the MacMillan Company, with an introduction by Robert Clurman. Drummond worked out of Malden, MA and had his underlings steal a body from Mount Auburn in Cambridge. Carter also faced Dr. Jack Quartz.
In A Fighting Man of Mars, Phor Tak. Originally sane while making his inventions, but losing it after being maltreated and exiled by his jeddak. At first it appears to be Revenge, but in the end, he reveals he wants to Take Over the World.
Garfield Reeves-Stevens' novel Dark Matter features a mad scientist cum serial murderer who actually manages to endow himself with metahuman powers similar to Captain Atom, Doctor Solar, Firestorm, and Doctor Manhattan (in imitation of the latter, he even visits Mars).
Remo Williams has encountered mad scientists, for example Dr. Judith White, who mutated herself into tiger/homo sapien hybrid.
His original goal was to remove/eliminate outright his "evil" side (the id). Unfortunately, one of the ingredients—a "special salt"—wasn't pure enough, and the resulting cocktail only worked halfway.
He gets a little mwahaha as Hyde:
Edward Hyde, about to drink the potion: And now, you who have so long been bound to the most narrow and material views, you who have denied the virtue of transcendental medicine, you who have derided your superiors—behold!
In the Soviet science-fiction story Amphibian Man, the title character's adoptive father, Dr. Salvator gives him shark gills, extensive knowledge about Oceanology and other sciences... and none whatsoever about such pesky details like days of week. Salvator also gives a rather passionate speech toward the end of the book critizising Science Is Bad.
Saruman can also be viewed as this character type, what with his obsession with industry at the expense of the natural world. He is also something of a would-be Emperor Scientist; he would have become one had his whole Take Over the World plan gotten off the ground.
The Corsay Books have a wide variety, from Frankenstein-style reanimationists, to those dabbling in Alien Geometries, to specialists in disciplines that seem closer to magic. They are the main antagonists of the work, but generally portrayed as misguided and dangerous rather than evil.
And he had to hide his genius or use it to play tricks with, when, with an ordinary face, he would have been one of the most distinguished of mankind!
The main character of The Chronicles of Professor Jack Baling is one of these. He doesn't start off as one, but by the end of the first episode, he resides firmly in this territory. There seem to be some other characters who are also Mad Scientists, but we haven't seen them in any great detail yet.
From Storm Front, the main antagonist has a whole factory producing a magically-laced drug. It's catalyzed by a ritual, fueled by sex.
Dr. Sacreya of Sacreya's Legacy is certainly mad, creating a zombie virus and all, but his intentions are good.
The Rings of Saturn has an old, very much insane scientist, living in the abandoned part of a space pirate base (without their knowledge) who is obsessed with researching other dimensions (and doesn't hesitate to send his lab assistant, or random strangers into them. Without giving them a way back.)
Qybourn of A Song of Ice and Fire is definitely this. He lost his title of Maester for experimenting on living people, and from the chapters in King's Landing, we get a good idea what these experiments involved..Let's just say that his creation of a Frankenstein-like creature mostly made up of Gregor Clegane is just the very tip of the nightmare-inducing iceberg.
The aeshes of A.L. Phillips's The Quest of the Unaligned have this reputation, and in fact in magickless Tonzimmiel, "aesh" means "certified engineer." Word Of God reveals that their secondary power is Haesh's Trace, a burst of insight that grants them true understanding of something they've been considering. An example of this is seen in Laeshana's sudden insight into the nature of magic while she is finishing her studies at the College of Magic.
The Solarian roboticist Jothan Leebig in Isaac Asimov's The Naked Sun. He's revealed to have been working on bypassing the First Law of robotics which prevents robots from harming humans by exploiting a flaw in the wording of the law. Leebig uses this to successfully plan and execute the murder of his colleague Rikaine Delmarre, who strongly disagreed with his vision, and attempt to poison both the newly assigned Solarian police investigator and Elijah Baley - the Earth detective. When he's forced into confessing, he also admits to have been planning on developing and building new war spaceships using this same exploitation of the positron brain in order to turn them into very dangerous and effective weapons.