"Courage" isn't a lack of fear. Courage is facing your fears despite being scared.
In the episode "Courageous Cure" Eustace and Muriel are abducted by multi-armed aliens so they can get a cure for a strange disease that causes them to punch themselves. By the end of the episode, it turns out that Courage's DNA was the one with the cure. This was because the disease causes people to punch themselves and 4 legged animals such as dogs do not have arms.
Other than that, Kitty spend most of the first half of the episode beating Courage, when all he was doing was minding his own business. His scream reaction to her identity was a TWO PARTER, if that needs any more indication.
While everyone knows Eustace refers to Courage as "Stoopid Dog!" (except for two exceptions), Courage himself never calls Eustace by name and only refers to him as "The Farmer." Coincidence?
As noted elsewhere, "Ball of Revenge" has Eustace complaining about Muriel giving Courage a newly-made blanket—his argument underscores the fact that he resents Courage because he's Muriel's favorite, as he said in "The Tower of Dr. Zalost".
In the episode "Perfect" the eel in the bathtub gives Courage a pep talk by telling him "There's no such thing as Perfect. You're beautiful just the way you are." When Courage accepts this, the perfection obsessed schoolmarm ceases to exist because there's no such thing as perfect!
In the debut of the character "Shirley the Medium," toward the episode's end Eustace learns a lesson in compassion after hallucinating a reflection of his upset younger self in a mirror crying for a hat to shade his head from the sun and being moved to actually sacrifice his trademark hat to the vision. There's spectacular symbolism in that scene...you have to learn to see yourself in the less fortunate.
Why is Courage so determined to protect Eustace and Muriel? Because the last time he was unable to protect the ones he loved he lost them forever, so he wants to ensure it never happens again.
In "Courage and the Mummy", how exactly did Muriel learn that cookie recipe she never knew before? Perhaps, in his former life, the mummy chef meant to teach the Mayan princess (Muriel's past life) the recipe for the cookies. But before he could teach her, the advisor (Eustace's past life) framed the chef. And the rest was history. By reenacting the scenario and fixing it, Courage virtually Set Right What Once Went Wrong, allowing the mummified chef to teach Muriel's past life the trade.
The Bagges are not always the first victims to fall into the enemies traps. Katz seems to provoke this the most which is evident with the bones littered all over the hotel in "A Night At the Katz Motel", the broken machines in "Klub Katz", and questionably the candies in "Katz Kandy". There are also other villains who have shown past victims as well, such as the skulls from "The Queen Of the Black Puddle", the puppets from "The Great Fusilli", the banana peel skins from "1000 Years Of Courage", and most infamously, the monster, bones, shackles, and "help" message from "Courage In the Big Stinkin' City".
Just what did Mad Dog do that made Kitty such a depressed wreck?
Aside from keeping her best friend a prisoner? ... Possibly a lot, actually.
When you consider part of the episode was an allusion to prostitution... the mind can fill in the blanks in the backstories.
Also, burying Bunny in a flowerpot doesn't seem too bad...until you realize that it's more than likely a Getting Crap Past the Radar metaphor that Bunny was gang-raped.
It's a (fairly) realistic portrayal of an abusive relationship. Those don't exactly leave a smile on people's faces.
Vastabael Backjurius's plan to stop the Bagges from fixing the sun is outright Monstrous if you have knowledge of life on Earth's dependance on the sun.
That and the rest of the solar system as well...
Although the very ending of "Remembrance of Courage Past" was Played for Laughs, we now know that Courage's parents are still alive. This is of course a good thing until you realize that they have no idea what happened to Courage or that he was adopted by a kind woman. For all they know, he starved to death after being left in the garbage by himself as an infant. Now, imagine being forcibly taken from your infant child and spending the rest of your life not knowing what became of him. That's extremely depressing.
Humans live much longer than dogs. What's going to happen to Eustace and Muriel when Courage dies?
Then again, considering how old Eustace and Muriel are, it could easily be the other way around.
Considering that Courage is an anthropomorphic cartoon dog, it wouldn't be surprising if he could live longer than a real dog is supposed to.
Made worse by the fact that earlier on in the episode, Courage found Fusilli's storage containing puppets hanging from the ceiling. Those puppets? They are hanging corpses, gathered from all his previous performances.
Benton Tarantella's character page describes him as "An evil zombie director who puts his "actors" in a position where they'll listen to everything he says where they can be Killed Off for Real on camera"...So, Benton has the honor of being the very first children's cartoon villain to make Snuff Films
As the show went on, Courage talked less and less and his speech was often just gibberish. We also see Courage take plenty of hits to the head during the series. Could it be in those later episodes that Courage is suffering from brain damage that has inhibited his ability to talk?
Eustace called in the Cajun Fox along with the rest of the villains in "Ball Of Revenge", despite the fact that the Cajun Fox episode was the only episode Eustace doesn't appear in. And he also calls in The Big Toe, even though he himself was The Big Toe.
About half the villains Eustace teamed up with tried to kill him.
The banana salesman appears in a later Katz episode even though he's supposed to be stuck in the next millennium.
Fridge brilliance, they've invented time travel a thousand years from the show's present time, he just hitched a ride back.