Genius Slob

A character of superlative intelligence and a superlative lack of hygiene. This type of character is seen at pretty much every variation of the alignment spectrum, and is usually associated with the image of the reclusive hacker. Usually, their slovenliness is combined with No Social Skills—whether it's a tendency for bluntness or extreme timidity, as well as a tendency for unsavory habits and eccentricity. Good guy genius slobs are usually portrayed as just being too dedicated to their vocation to have much time for hygiene, while the filth on bad guy genius slobs is used as an outward reflection of inner rottenness.

Keep in mind that this is not a genius who is constantly filthy because of his job. A genius engineer who's constantly dirty from working on machines is not a genius slob, he's just dirty because in his line of work it's inevitable. This trope specifically refers to geniuses who are filthy in their personal lives. It's not a consequence, it's a character trait.

Examples of Genius Slob include:

Anime and Manga

Kosuke Entouji of GaoGaiGar could pretty much be the ultimate example of this trope. A very good guy, essential to the 3G's operations as their information analyst, and thoroughly disgusting hygiene. His workspace is a total mess of empty snack bags and magazines (not to mention many fans have suspicions about that box of tissues...), and he'll go for days at a time without taking a bath. Every time he scratches his head, a cloud of dandruff erupts from it.
The Hacker from the old AD Police OVAs, who was overweight, always barefoot, and could barely move within his apartment from all the crap lying around.
Death Note: L, while not as filthy as other genius slobs, is VERY eccentric, a challenge to have a conversation with, and always has a disheveled appearance and bare feet. His eating habits leave a lot to be desired, too.
Dr. Greg "Bear" Eagan in Eureka Seven is a reclusive, slovenly, colossally fat man who only seems to eat candy—and an absolutely brilliant scientist.
Supervisor Komui from D.Gray-man. Science genius and one of the most important members of the Black Order. So disorganized you can't see the floor of his office.
Hakase from Mahou Sensei Negima. She sleeps in her lab sometimes and leaves her underwear lying around, which gets comments from the guy scientists who share the lab.
Erica Hartmann from Strike Witches: one of the squad's top aces in the air, lazy slob on the ground.
Dwun from Hunter X Hunter.
In Eden of the East, the genius programmer Yutaka Itazu just put the finishing touches on a computer-program that can predict the future. He also lives in an apartment that's so messy he's practically had to dig tunnels though the rubbish, never leaves it, and never wears anything but underwear. His excuse is that his only pair of pants blew away when he was drying them, hence his nickname of 'Pantsu'...

Film

From Jurassic Park, both food addict networking director Dennis Nedry and chain-smoking control room chief John Ray Arnold.
In the first Spider-Man movie we get this exchange, upon entering Peter's room.

Norman Osborn: Bit of a slob, isn't he?
Aunt May: All brilliant men are.

Literature

Sherlock Holmes: Holmes, of all people. Yes, his living room and general appearance to the public is neat and fastidious, but walk past the curtain into his study and you'd be flabbergasted at the enormous clutter of evidence and experiments. The 2009 Guy Ritchie-directed film starring Robert Downey, Jr. illustrates it excellently, and in the modern version Holmes drives Watson crazy by, for example, keeping severed heads in the refrigerator and eyeballs in the microwave.
- Holmes is a slob with respect to his home and belongings, but not in his appearance—in fact he is said to have a "catlike love of personal cleanliness".
Plague, Lisbeth's hacker friend in The Girl with the Dragon Tattoo, is balding, overweight, smelly and supposedly has a porn collection to baffle minds. He's also a genius with computers (both their construction and programming), and is a master investigator, able to get information for Lisbeth that she has a trouble finding (or getting access to).
Tokita of Paprika. He's fat, clumsy, and his work area is a mess. Doesn't stop him from getting the girl in the end, though.
Mary Gentle's character Baltazar Casaubon: A brilliant architect and/or hacker (depending on the exact story)...who's almost invariably either freshly bathed, or absolutely covered in dirt, grease, and food stains.

Video Games

Otacon in the first Metal Gear Solid game, was prone to this. He cleans up in the sequels though.
Apple Kid from EarthBound.
If teamed up with a particular homie, ex-FBI hacker Kinzie Kensington in Saints Row: The Third reveals she doesn't even know how to wash her hair.

Real Life

Michelangelo was a real life historical example. He apparently only took a bath twice a year or so, something considered disgusting even in those days.