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.
Awesome Music: The theme song, which is often considered the best part of the show. Even people who hate the show agree that it's good.
Dude, Not Funny!: Cat is always the one who suffers the most from his crazy friends/enemies, but especially Dog's dog-like antics. It's even sadder how Dog just watches as his brother is brutally skinned alive several times without doing anything.
Ear Worm: Cat-Dog, Cat-Dog! Alone in the world is a little Cat-Dog!
"A pretty little piece of paradise / That's a-where I wanna be..."
Nightmare Fuel: In "Dog's Strange Condition" where Dog has a tree growing on his head after having allergens with pecan pies.
In "Fishing For Trouble" Cat goes into Dog's mouth to find his fish Veronica. Near the end, he goes to the mouth of another Cat that screams in response, and later discovered Dog's fish mutated and then it eats CatDog from the inside.
In "The Collector", where Cat is persuaded by his Mean Bob toy to start a collection, and then beaten up by his Mean Bob collection to prevent themselves from being sold.
"Teeth For Two", like when Cat temporarily becomes skinless, and other parts of the episode.
Dog's grotesquely over-muscled form in "Pumped".
The episode where Cat loses his brains.
In-universe with Dog in the episode "Nightmare".
The Scrappy: Winslow and Rancid Rabbit appear to be this, since they almost always ruin CatDog's day.
Cliff of the Greasers, as well. Shriek is more of a Base Breaker, as she has a few good moments with Dog, and Lube averts this, due to having a few episodes in which he is not an antagonist (and a lot of other instances of being too stupid and ineffectual to be malicious otherwise). Cliff, however, is just a Jerk Ass (though to compensate, he arguably has the most frequent moments as The Chew Toy).
Tear Jerker: The parents' flashback in The Great Parent Mystery.
Also that one episode where they have to build a brick wall between each other.
They Wasted a Perfectly Good Plot: The Great Parent Mystery. It had a lot of build up to it, and generated some interest into the identity of CatDog's parents. Only it turns out that the bigreveal was that we get to see CatDog's adoptive parents. One could imagine a few people being annoyed by this.
Unfortunate Implications: The Greasers constant beatings of CatDog, especially Cat reeks of racism and/or general prejudice.