These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Yuck: You can't beat my pants! Thanks to Yin they're in a very naughty mood.
Anvilicious: Mocked with The Lesson, a villainhero who tries to hammer home aesops into people's heads (mostly Yang) with little success because even the people who agree with him (Yin) think he's an out-of-touch, overbearing jerk.
Awesome Music: The opening title card music is pretty impressive.
Fan Nickname: Some of given Yuck's nicer personality in "Upstanding Yuck" the name Oliver; also, Yin's evil side in "Gone A Fowl" is sometimes called Eve.
Fanfic Fuel: The show offers a plethora of these. But perhaps the most notable is the twins' mother, which was teased in one line of dialogue at the end of the series finale, "Yin Yang Who?"
Foe Yay: Many fans believe there is this between Yin and Yuck.
In "Falling Yin Love", they even kiss each other and when Yin claims she "wants to be close to him" only to drain his Woo Foo with the same gloves he used on her he looks pretty happy and smiles.
There's also the fact that he always seems to be involving Yin in some way in his plans. This especially happens in "Falling Yin Love" but there's also "Camp Magic Pants" where he devises for Yin to become evil by using her magic for wrong purposes so she can touch the golden pants statue and allow him to control it; even so, he jokingly thanks her.
There seems to be some on Yin's side as well, especially considering her interest in bad boys. In "Falling Yin Love", after Brett is revealed to be Yuck in disguise she seems heartbroken.
Yin: But, I thought you liked me.
Yuck: Brett did (kicks robot head aside). But Brett isn't here anymore.
Yin: (cue tears)
Ho Yay: Roger Jr's secret desire to be Yang's friend turns into this at times, especially in "Splitting Hares".
Jerkass Dissonance: Yuck has quite the large fanbase despite the fact he's called a jerk almost constantly.
Les Yay: Saranoia's obsession with Yin certainly leans into this, especially prominent in "The Truth Hurts".
The Night Master, whose plans usually only fail because he's Surrounded by Idiots, but pulls off a number of successful schemes.
Yuck's plan in Camp Magic Pants has shades of this:
First, he possesses the body of the headmaster of the camp, taking control of it and sending out a messenger to invite Yin and Yang there.
Next, he puts the twins in separate cabins so Yin could become infatuated with Terry Otter who happens to be another pawn to the plan to make Yin use her magic for bad purposes.
Lastly comes the games which he purposely sets up to have Yin cheat, making her entirely naughty enough to touch the golden pants statue. This is when Yuck reveals himself and takes the golden pants for himself without being known until the end. He still lost but it was a pretty elaborate plan.
Moral Event Horizon: Ultimoose once he becomes the Nightmooster in "Deja Foo": he not only destroys the entire town but he kills Master Yo and Yin by burning them to death; to add insult to injury, he does it right in front of Yang.
Ron the Death Eater: Lina at times get's this treatment: although she's simply a Tsun Dere character with a sassy personality, she's a generally nice girl and helps her friends in saving the world later; but to the fans, she is a selfish, uncaring bitch who wants Yang all to herself. Fanfictions often depict her as a terrible girlfriend, making sure that Yang's romance with the writer's Relationship Sue can occur with Lina out of the way.
Self-Fanservice: Yin receives plenty of fanart depicting her as a well endowed teenage girl in skimpy or tight clothing; this mostly started to spring up after her Plot-Relevant Age-Up in one episode where she becomes an attractive teenager.
Yang and Carl are stuck together and an ersatz version of the theme to The Odd Couple plays.
There's a chase scene wherein the music is a near-miss of "Yakety Sax".
They Wasted a Perfectly Good Character: Ever since the first episode he appeared in, fans instantly loved Yuck to the point they wanted him to be a part of the main cast or at least be involved in far more episodes; though he isn't entirely wasted, out of the fairly lengthy seasons, he only appears in six total.
Yuck in "Upstanding Yuck". All he wanted was to make friends with Yin and Yang and to prove he had become a good person. Throughout most of the episode, he suffers beatings from Yin and Yang without once getting mad at them. It's only until the end that he cracks and goes back to his evil ways. Still, you can't help but feel bad for him.
Yin and Yang are also this in "The Confidence Game" where the majority of the episode has the two of them being horribly beaten by Eradicus and his Quirky Mini Boss Squad in a week long losing streak. Yin and Yang are at least 11 or 12 years old and their enemies are obviously older than them; also, the latter group seem to have an unsettling joy in beating the former.
And then their master and father figure fakes his death in front of them to force them to fight for themselves. Poor kids can't catch a break!