Inspired by this post. Every show has the extreme character.
Big Bang has Sheldon
Seinfeld has Kramer
House has House
Back in the day, there was a show called Soap.
The extreme character was … everyone (except Benson).
Cowboy Bebop had Edward.
I wouldn’t say every show has one, but they are common. Some are:
Lucy in I Love Lucy
Gracie in The Burns and Allen Show
Gilligan (and probably Thurston Howell, too).
Maxwell Smart
The Great Gonzo
And before he was Gilligan, Bob Denver was Maynard G. Krebs in Dobie Gillis.
All in the Family had Edith
The Bob Newhart Show had Mr Carlin
Happy Days had Fonzie
The Mary Tyler Moore Show had Ted
MASH had Klinger
Taxi had Latka and Jim
Can you tell I grew up in the seventies?
How I Met Your Mother has Barney Stimson
Fringe has Walter
The office - probably Michael Scott and Dwight Shrute are the ‘extreme’ ones, both.
Prison Break-Theodore Bagwell(T-Bag)
My Name is Earl-Donnie Jones
Urkel from Family Matters
The Odd Couple. Both Felix and Oscar, extreme and opposite.
Newhart had Larry, Darryl, and Darryl.
Jane Deaux on Dharma & Greg, put there to make Dharma look normal enough to plausibly be happily married to Greg. Played by the delectable Shae D’Lyn.
And Phyllis. And Rhoda. And Sue Ann.
And Larry. And the guy who thought he was a poet, and the guy who thought he was a cat.
*Everybody Loves Raymond *had Marie.
*Celebrity Jeopardy! *had Sean Connery.
*Star Trek Voyager *had Neelix.
*Will & Grace *had Karen and Jack.
*Monk *has . . . well, Monk.
The West Wing had Aaron Sorkin.
I disagree. She wasn’t any more “out there” than the rest of the clan, although she was certainly the most controlling.
If you’re going to pull someone out of ELR, it would be Amy’s brother Peter MacDougall, played by Chris Elliot.
Monk has Monk, and Randy Discher, and the annoying neighbor guy who can’t tell a story without telling everything going on about him (who is, thankfully, dead now), and the other neurotic guy that Monk competes for to be the most neurotic.
Actually, that’s one of the major flaws of the show - too many extreme people. I know, it’s a comedy, it still is too much. One nutbag per show, please.
Buffy tvs - Anya 
That Poochie was one outrageous dude.
Dukes of Hazzard has Boss Hogg