Basic Trope: A female character falls in love with or feels very attracted to a 'bad boy' (i.e. a male character with dysfunctional, aggressive or outright criminal character traits), usually choosing him over a 'nice guy'.
Straight: The female character falls in love with a convicted criminal.
A woman falls in love with a man because he forgot to pay a parking ticket (or some other similarly minor 'bad' trait), this making him a 'bad boy' in her eyes.
Alternatively: a man goes to ludicrously extreme lengths to present himself as a 'bad boy' in order to attract a woman's interest. This includes kicking babies in the face, setting kitties on fire, blowing up buses full of nuns, and playing whiny protest songs from the 60's. And it works!
Alice has an obvious crush on her friend Bob, the bad boy of the school (he has yet to tell anyone but Alice that he just likes the fashion), but then Bob's put into a situation that is out of the law's hands. Alice is against all of this, seeing that it's changing him, and abandons him. Later, she gets attracted to him anyway. She's also attracted to Charlie and Bob gets a new friend, Darlene. Charlie has his eyes more on Darlene than on Alice. The Creators try to get Yaoi demographic by introducing Eddy who's involved in a Ho YayLove Triangle with Bob and Charlie. Alice and Darlene also have their own Les Yay going on.
Alice in love with Bob the Jerkass, but then it turns out Charlie the so-called "nice" guy is an Unreliable Narrator who is in love with Alice. It turns out the person who called Charlie out was the real Unreliable Narrator all along. However (s)he wasn't lying about Charlie making up all that stuff up about Bob. Then it turns outs he wasn't making all that stuff up, Bob was just picking on Charlie because he hates his guts.
Averted: There is no single 'bad boy' character; the woman's romantic options are between flawed but decent men.
Enforced: "We need to soften this criminal character up, so he has a reason to clean up his act. Maybe make one of the supporting female characters fall for him?"
Lampshaded: "Of course, she loves him; bad boys are sexy, everyone knows that!"
Invoked: A guy tries to build up a bad boy image to get a girl to like him.