One hilarious example of taking responsibility for stained clothing happens in History of the Salaryman, when a waitress spills a tiny drop of coffee on Baek Yeo Chi's designer shoe. She immediately asks "Do you know how much this shoe is worth?!" in a tone of voice implying it's worth more than the unfortunate waitress' entire family. She then uses the incident as an excuse to throw a massive tantrum in the cafe, likely unleashing a tirade that would make the most hardened sailor blush, if previous experience of her swearing abilities is any indication.
Later, when Yeo Chi is living on the streets, a woman bumps into her, causing her to drip milk on her boot. The woman echoes Yeo Chi's earlier question of "Do you know how much this is worth?!" Yeo Chi scoffs at her, and on closer examination of the woman's boot says that it's a knockoff and not really worth all that much. In fact, from head to toe the woman is dressed in knockoff labels. Yeo Chi tells her that despite her appearance, she is the Label Queen, and knows Versace on sight, and that, my dear, isn't Versace. She then turns the tables on the woman, asking "Aren't you going to give me fifty cents to pay for the milk you made me spill?"
This woman didn't really expect a homeless person to be able to replace/pay damages for her clothing, knockoff or no, did she? Seriously? A problem I have with this attitude in dramas is that it's almost always the super rich asking someone to pay for damages, often expecting the person who caused the accident to arrange the dry cleaning themselves. Really?! What's that going to accomplish? I mean, you were already going to have to have it dry cleaned eventually, and you probably have an excellent and trusted (and expensive) dry cleaner that you use. Are you really going to trust this random person with almost no money to take your precious article of clothing, one that you may never wear again anyways, to some random and cheap dry cleaner in their neighborhood? Or do you think that financial compensation is really the best solution? I know it's a matter of pride/honor, but it's almost always an accident, and a small one at that.
Another common way to take responsibility is after causing an injury. In I Do, I Do, Tae Kang punches Eun Sung in the face. Eun Sung demands payment for medical treatment, including costs for emotional trauma, and says that Tae Kang loosened his teeth, which he'll have to get treated.
Ha. He punched you on your pretty cheekbone, buddy, not your mouth. Granted, Eun Sung is trying to teach Tae Kang a lesson on Being an Adult and Offering a Proper Apology. Even though Tae Kang is overstepping his bounds, Eun Sung is being incredibly petty.
In I Love You and I Do, I Do, taking responsibility for pregnancy is a driving plot point. It comes up in plenty of other dramas, but I can't think of any right now. In the first episode of Big, Gil Da Ran asks Yoon Jae if he's just marrying her because he's taking responsibility or if he loves her. This leads us to believe that it's because they've slept together (it didn't seem to me that she might be pregnant, though), and thus he proposed in order to protect her honor. However, throughout the course of the next few episodes, it becomes clear that their relationship hasn't reached that point yet. Kyung Joon realizes that Da Ran hasn't even seen Yoon Jae's chocolate abs, nor had they progressed beyond one chaste (and on her side sleeping) kiss. We then learn in a flashback what Yoon Jae meant when he offered to take responsibility—he feels guilty that he caused Da Ran to fell down the stairs and missed the opportunity to take her teacher licensing test as a result. As this could potentially impact her entire life, taking responsibility involves providing for her by marrying her. (On a side note, it's still unclear to us whether he had genuine feelings for Da Ran or was marrying her out of a sense of duty.)
However, my favorite use of the idea of taking responsibility comes from My Girl, in an awesome reversal of the trope. One night, Yoo Rin comes home to a quiet house, and Gong Chan informs her that everyone is out for the night, so they'll be staying there alone. Yoo Rin rushes up to her room and suddenly starts having ideas. She is worried that she'll be unable to control herself alone in a house with such an attractive man (I feel for you, sister), and in her head imagines a situation where she is the one who has to take responsibility for him. Gong Chan is hiding under the comforter wailing and rolling around, now that he is "damaged goods", and she tells him in her manliest voice not to worry, she'll take the responsibility, and to stop crying. After creating this mental image, she proceeds to barricade herself inside her room.
Overall, using the concept of taking responsibility can be a very useful tool in dramas. It effectively creates tension, provides characters with motive, drives relationships forward, and contributes to great comedic situations. I hope using it appropriately in dramas never goes out of style.