The Prosers: the office

Barney Stinson.

This man is horrible. He's the kind of character that you love to see slapped, because he more than deserves it. He works for an evil...no, the evilest corporation ever, and he loves it. He's oppurtunistic, and manipulative. He's a lying womanizing jerk, with little idea of boundaries, or how to do what's appropriate. He's dot on the Jerk/Hot scale is so far off, it's unbelievable.

How the creators of How I Met Your Mother made him likable.

They gave him a history of pain, and explained why he's the way he is. Harmful mother, Jerky ex girlfriend... the works.
They balanced his badness with awesomeness. This guy ran the New York marathon without training. He is as awesome as he say's he is.
They gave him a code...the bro code... of conduct. There's a line that even he won't cross...Except that one time when he did.
He would do anything for his friends. He got hit by a bus for his friend. He put on an entire four hour long horrible play for his friend. He's loyal.
He's a child. He's an emotionally stunted fifteen year old in a designer suit.

Gregory House

He's a drug addict. He's a jerk. He's a narcissistic, manipulative, criminal who will do anything and nothing to help save a patient. He's also brilliant, broken, in pain, and you will buy him doing or saying anything. He's the kind of character that regularly says things so awful you wouldn't even think them, and the other characters are so used to working with him, that they don't even react anymore.

How the creators of House made him likable.

He's in pain. He's hurt. Not only his leg, but also he's emotionally scarred from his upbringing.
He's lonely. He's the only person he know's who is as smart as he is, he pushes people away as a test, and it's a test that most people pass.
He's as smart as he thinks he is. The only thing he cares about is being right. And he is almost always right. He does whatever he wants. Also, there's something appealing about watching a character do something that you wouldn't even think of doing.
Wilson stay's with him. He has a good honest friend that sees something redeemable, and enviable, inside him.
He's an emotionally stunted child.

Sheldon Cooper

He's insulting. He's narcassistic. He's so annoyingly particular, and always right. He has no humility, or compassion. He is... in a very real sense... a robot. A brilliant, obnoxious, robot.

I love him.

Here's how the creators of The Big Bang Theory made him likable.

As brilliant as he is about...most everything, he's also a complete failure at social cues. He doesn't get sarcasm. He doesn't get most jokes. In fact...he basically doesn't get anything about the world he lives in.
He's a child. And not only is he a child. He's a bullied, slightly pathetic beaten puppy of a child. He's the kind of character that you just want to hug, except you know how uncomfortable that would make him.
He's as brilliant as he thinks he is. He's not just a boaster, or a fake.
His friends, even though they get the brunt of his punishment, and awkwardness, would still do anything for him. He's loved and accepted by likable characters...even if it's hesitantly. Penny singing Soft Kitty to him, does as much for his character in likableness as it does hers.
He's an emotionally stunted child. Yes, I said it twice. Have you met Sheldon? It's the history of pain, that explains and excuses his behavior.

Michael Scott

He's needy. He's inappropriate. He's selfish. He would be manipulative, but he's not that smart. He's a time waster, the antagonist of productivity. He's so mean to Toby. He's a failure at basically everything he ever wanted to do, yet he's still at a higher rank than the rest if the office. He's also the creator of Blind Guy Mcsqueezy, Prison Mike, Ping, Michael Clump, and (my favorite) Agent Michael Scarn.

How the creators of the Office made him likable.

A history of pain. He comes from a broken home. He never had any friends and was a lonely forgotten child.
He's good as what he does...Well, maybe not managing, but he was the best salesmen ever at Dunder Mifflin, and he's genuinely a good salesman.
The likable characters at the office grow to like him. Jim and Pam's approval of him, while slowly earned, makes him likable.
He's made fun of behind his back, and treated poorly, the butt of the joke for everyone in the office. He's treated worse than he treats others, and that imbalance makes you root for him.
He's an emotionally stunted child.

Reginas

It took me a while to think of an unlikable female character that I actually liked, and that say's something... Why is it more difficult to write a likable bad girl character? There's the Evil Queen...Regina on ABC's Once upon a Time, and then there's the evil Queen...Regina from Mean Girls... And... hmm... Maybe Jenna ( is that short for Regina?) from 30 Rock. Moral of the story... don't name your daughter Regina.

Anyway, so Regina George/ Regina (Evil Queen)/ Jenna are beautiful, powerful woman, who aren't afraid to hurt someone to stay at the top of their School/Town/ Fame.

How they make them likable.

Regina George had to get hit by a bus in order to become likable. Evil Queen Regina had her love killed by her mother. Jenna is... an emotionally stunted former pageant queen whose mother used her winnings to buy booze.
They're beautiful. It's sad that it's true, but characters can get away with a lot more if they are physically attractive. Especially female characters.
They aren't treated well. People talk about them when they aren't there. They mock them, they hate them, they envy them. People seek to destroy them. If the balance is pushed past equity, then you can like them.
They are as powerful as they think they are. They aren't fake.
They are emotionally stunted children.

Okay, so you can see a recipe for creating likable despicable characters. At least likable male characters.

As writers...and as women... we need to write more awesome well rounded female bad guys. The world needs more female characters who can say and do anything they want to do. Characters who are smart...so smart that they are annoying. Characters who have emotional back stories that shaped them into characters with broader boundaries of right or wrong. Emotionally stunted little girl children who lash out and throw fits, or have a good cry, and won't hesitate to destroy/ annoy/ or abandon. Maybe even...dare I say it...in tennis shoes or slippers- not high heels.