There's a fan theory that states that the events in the show are just normal events as seen from a dog's perspective. Some specifics of the theory include:
Courage actually lives on a regular farm. He just thinks it's in "the middle of nowhere" because his owners are too old to walk him and he doesn't know what's outside.
The "monsters" in the show are just normal people or objects that Courage imagines as something completely different. That would explain why Eustace and Muriel rarely seem to notice any of them. Courage is actually freaking out over a postman, or a vacuum cleaner.
There exists a theory that Eustace is jealous of Courage for "stealing" Muriel's affection from him.
Awesome Music: The Tower of Dr. Zalost's haunting leitmotif, to the point that it's sometimes the only thing that can be heard, even when the titular character is firing cannonballs at our hapless hero.
Base-Breaking Character: Eustace. He's either Jerkass Woobie who's only grouchy because of his rotten childhood or a total asshole who doesn't deserve any sympathy. There are also fans who think he's kind of funny (at least, the funniest of the main trio), but others find him irrationally cruel to his dog well past the point of humor.
A flying dragon coming out of absolutely nowhere (pun not intended) and eating Eustace in the last five seconds of the episode.
Eustace getting mauled by a Siberian Tiger while deer hunting.
Seems as though animals are always coming out of nowhere to attack Eustace, as he got attacked by a giant squirrel in "Family Business".
Most of Courage's nightmares from the last episode could count, especially that blue thing. It really had no importance to the rest of the episode except to scare you straight and it really wasn't seen or mentioned again in those other nightmares.
When Eustace gets cursed by Shirley the Medium to always have a black cloud following him, at one point he passes a man poking his head out of an alleyway. The man is being strangled by a green tentacle and hurriedly asks Eustace if he will deliver a message to his fiance that he won't be able to make the wedding. Eustace completely ignores him and the man is whisked down the alley by...whatever that was. It has nothing to do with the plot other than to show that Eustace is still a selfish asshole.
Theway Katz gets defeated in "Katz Under the Sea".
"Snowman's Revenge" has Snowman breaking out into a So Bad, It's Good musical number about... a chilly love story? Huh?
"Courage Meets The Mummy" opens with an archaeologist dusting off a gem inside the Mayan temple, which then shoots out a beam of light which gets reflected off some things and causes a disco ball to come out of the ceiling while some music plays for a brief moment. Afterwards, the archeologist just shrugs it off and continues dusting off the gemstone.
In "The Magic Tree of Nowhere," Courage digs a moat around the tree and adds Instant Eel to the water. Thatmakes sense in context. The eel then singing "Danny Boy"...not so much.
Immediately after King Ramses summons a horde of locusts, Muriel rushes into her kitchen in order to prepare food until she becomes exhausted. There is absolutely no reason for her to do this and nor does this even correlate with the rest of the episode. The only reason one would assume she does so is to prevent it getting eating from the locust, but even then...
The violin girl in "Courage in the Big Stinkin' City".
Broken Base: Season 4's "Ball of Revenge" is arguably the most controversial episode of the entire series. On one hand, fans enjoyed seeing many of the villains (including Katz, Le Quack, and the Cajun Fox among others) return towards the series' end to seek their revenge, and consider it one of the best simply for being one of the darkest episodes of the series. On the other hand, many other fans considered it to be a huge missed opportunity by leaving out so many other villains that were all still alive last time they were seen and had lingering grudges against Courage and his family (like Tarantella or Schwick). Plus there's the fact that Eustace was the one leading them which many fans thought was far too cruel and straight up evil of him to actually want to kill Courage over something as minor as a blanket. Finally, several of the villains returning made no sense in context considering that some of them actually tried to harm Eustace specifically in the past (the Queen of the Black Puddle), were just mindless animals with no motivations (the Weremole), or had no possible way of being there in the first place (The Clutching Foot was Eustace's foot fungus that took over his body)
The conclusion of the episode seems to be a base-breaker as well: Courage screaming at the top of his lungs for almost a straight minute to defeat the villains is either awesome because he takes them out all at once in a way probably no one expected, or it sucks because it's so out-of-character for Courage to use his screaming as a weapon rather than outsmarting the villains like he usually does. To be fair, this was the same way he would defeat the evil veterinarian in "Remembrance of Courage Past", and that wouldn't cause any controversy.
Cargo Ship: In "The Gods Must Be Goosey", the Goose and Eustace's Truck are getting married at the end of the episode.
The Great Fusilli, from the eponymous season 1 episode, is a traveling stage magician who lured people onto his stage under the guise of making them famous actors. He would then have them perform for an imaginary audience, in order to use enchanted puppet strings to convert them into lifeless puppets, which he would then play with for his own amusement. Once Courage finds a room filled with the dozens of people he's converted into marionettes, Fusilli turns his owners Muriel and Eustace into puppets while at the same time attempting to dispose of Courage. Although Negative Continuity undoes the effect of Muriel and Eustace's murder, the ending of the episode leaves disturbing implications. Though comparatively minor compared to more major villains of the show, Fusilli was on par with even Katz, and his one appearance in the show proved to be one of the most disturbing episodes of the show's run.
The music that plays during Katz and Courage's tennis match in the first episode.
The music playing when Schwick chases Courage and Muriel in the episode "Courage in the Big, Stinkin' City".
Dork Age: Season 3 is generally considered the weakest season of the series, having few episodes that were as good or memorable as "King Ramses Curse", "Freaky Fred", "Ball of Revenge" (which, for all it's controversy, stands out more than most of season 3's episodes), "Courage In The Big Stinkin' City", "The Mask", "Remembrance of Courage Past", "Last of the Starmakers", "A Night At The Katz Motel", "The Tower of Dr. Zalost", "Evil Weevil", and "Perfect".
Genius Bonus: The difference between the words "bravery" and "courage" is that a brave man isn't afraid to start with, while the courageous man is afraid but does what has to be done in spite of his fear. That's Courage the Cowardly Dog in a nutshell. And it's why he's awesome.
Courage's last lesson in "Perfect" is to draw a perfect six. Six seems like an arbitrary number, until you realize it was chosen because six is a perfect number.
The Mission To The Sun became some sort of prediction to Sunshine due to both of their premises being on a mission to rekindle the sun while being sabotaged by another person (Pinbacker for Sunshine and the worm for Courage).
Courage is named "Leone" (lion) in Italy, because of his courage. He lives in the middle of the desert, he rarely talks (if ever) and is extremely loyal to his owners. Then a certain cartoon comes in, where the protagonist meets a pink lion in a desert who never says anything and is extremely loyal to his owner.
The Queen of the Black Puddle has feasted upon many men by using her supernatural charms to lead them to their doom. Whoever followed ended up as a grinning skeleton in her garden of death.
Ma Bagge abused and neglected Eustace through most of his childhood. Bad enough, but far from her only candidate. In Bad Hair Day he kidnapped and experimented on people for her firm, in the Mc Phearson Phantom she planned with the titular phantom to cripple Eustace and frame Muriel, she intended to abandon the Bagges to a sand-whale in The Sand Whale strikes and attempted genocide against and underwater population of little smurf-like creatures for her firm's sake in Scuba Scuba Doo.
Di Lung has proven to be a total sociopath, when he had his robot brutally beat up Courage, kicked him in a manhole out of spite in another episode and also removed Muriel's bones for a dark ritual, laughing while he did it.
The idea of on of the Valkyries falling in love with the incredibly disgusting Troll king, and soon the other Valkyries and the trolls falling in love is just, gross. Don't think about their Honeymoon to much...
That scene doubles as a Crowning Moment of Funny because the as the Valkyrie and Troll King were singing about how much they love each other, they would not. Stop. Singing, Despite the fact that the rest of the Valkyries and Trolls were on their way to the cave. Added bonuses include going to the scene of the Valkyries and Trolls running their way over there, and cutting back to the Valkyrie and Troll King, STILL SINGING, and cutting back over and over, but also Courage Lampshading it.
The Violin Girl in "Courage in the Big, Stinkin' City".
King Ramses' in "King Ramses' Curse".
What Do You Mean, It's for Kids?: A lot of people probably think Courage is for an adult audience with all the strange horror and black comedy. One extreme example of this is the episode called "The Mask", which is basically a cross between a psychological thriller and a gangland drama. And that's not even mentioning how abusive Eustace is to both his wife and his dog on a regular basis.