In the case of Zim, does he have the potential to be a good invader if it weren't for his ego getting in the way or has he burnt-out? Likewise, is he truly an evil being or is he merely a product of his environment?
Why doesn't anyone believe Dib? Are they genuinely stupid or has Dib cried wolf one time too many?
Author's Saving Throw: Vasquez admitted that he'd made Membrane and Gaz's abuse of Dib just a bit too cruel. It was toned down quite a bit in the comics and Enter the Florpus. Only, of course, so the joke would be funnier.
Dib. He's either The Woobie or a whiny, annoying, brat who deserves all the shit he goes through and then some.
Big Lipped Alligator Moment: In "The Girl Who Cried Gnome" there was an incident where Zim let loose a "Robot Gopher" to get rid of a girl scout that had wandered up to his front door selling cookies. After burrowing underground and trapping the girl's foot in a hole the Gopher proceeds to dance with her and then flew away into a swirling vortex leading to another dimension.
Zim: "I don't remember programming that..."
In "Gaz, Taster of Pork," Dib goes to MacMeaties and talks with a hobo. But wait for it... he spontaneously kidnaps a poor guy eating there. We never see the hobo again.
And then there's that Ham Demon in the Tak episode. Shows up for one scene, fights Zim, never mentioned again.
The idea of Dib and Gaz being Artificial Humans. Some think it's in character for Membrane, others feel that the Membrane mother could have been a rather interesting character (usually fancast as looking very much like Gaz and sharing Dib's passion for space).
Professor Membrane, so very much. He has a switch that restores power to the entire earth, flies and shoots energy blasts when excited, builds and refuses to use a perpetual energy device on a whim, etc.
Dib and Zim piloting Mercury and Mars, respectively, as ships in a space battle for the continued existence of mankind.
Cult Classic: Despite its cancellation, it still got decent money from merchandise more than ten years after the plug was pulled. Not to mention the huge, still-alive fanbase.
Just to drive the point home: to commemorate the 10th anniversary of the show's debut, fans recently held the first "Invader Con", which is exactly what it sounds like - an entire convention dedicated to the show featuring several of the voice actors as guests.
Tak's only in one episode (and an unrecovered script), but in fanfic she often gets billing as a main character. She is the only significant female Irken.
Counselor Dwicky from "Vindicated" is similarly popular.
GIR is popular to an absolutely absurd degree. To go by merchandising, not only is he the most popular character in the show, his popularity might actually exceed the show's, as people have been known to buy GIR memorabilia despite having never seen Invader Zim. As the creators themselves have gone on record saying, "America loves GIR!"
Keef and Gretchen also have become rather popular. Albeit not the level of Tak and Dwicky.
Almighty Tallest Miyuki is quite popular for someone who never appeared.
The Irken Empire spans galaxies, with who knows how many Invaders running around destabilizing planets?
Fanon Discontinuity: "Gaz: Taster of Pork" gets this treatment quite a bit, due to the Idiot Plot and both Dib and Gaz acting out of character. In fact, even the creators themselves label it as the worst episode of the lot.
"Mopiness of Doom", though never animated, was full of this.
GIR (to Dib): Listen to me, he [Zim needs you Mary! You two such good friends! Like hot dogs! Please hunt my master again! COUCH!!]
Sort of gets a look in the series with Dib's initial crush on Tak, a ruthless and competent female Irken who shares his hatred for Zim (if not exceeds it) but is planning to conquer/destroy Earth herself as part of her plan to discredit Zim. Of course, she only showed up in one episode and Dib seemed to lose any attraction to her after discovering she is also an alien invader.
It's never explicit that Dib likes Tak, though that's a popular fan interpretation; the two act friendly and he tells Zim he "likes" her, but he could easily have meant it platonically. He gives her a valentine and Gretchen, who likes him, is clearly upset, so there's at least a slight aura of crush.
With Steven Universe, given that Rebecca Sugar is a fan of Zim (she even wrote fanfictions!) and may have based Peridot on him. That said, some Zim fans are not so eager about Steven Universe since most of the art of the two shows is just Zim and Peridot.
Hilarious in Hindsight: In one episode, Zim catches Dib sneaking around his house in a squirrel disguise. After Dib runs off, Zim yells a parting insult to him, calling him "Squirrel boy!" Several years later, Zim's voice actor would go on to voice the titular character in the series Squirrel Boy.
This, when you consider the internet meme involving trollface an "u jelly?"
Dib: You're just jealous...
Zim: This has nothing to do with jelly!
Hype Backlash: As it is with everything popular, there will always be an internet cynic who thinks the show is overrated.
One criticism is that most fans of Zim seem to be hyperactive "I'm so random" 12-year olds who only like the show because of Gir. This certainly isn't true, as there are many other older, more mature fans out there who appreciate the show for its dark, twisted sense of humor.
Internet Backdraft: And how.Operation Head Pigeons was first started on Facebook, and still remains a group as Operation Head Pigeons 2.0. Nickelodeon says that they've never seen a fanbase as hardworking as them. They've most likely triggered a DVD release, and through whatever miracle, possibly could revive the show. (Though this idea seems to be on the backburner now.)
Jerkass Woobie: Zim, for some. Dib for some more, though he'd be easier to argue as a regular Woobie.
Misaimed Fandom: Some of Zim's fans have the tendency to play him up as The Woobie while entirely glossing over the whole "Kill All Humans" thing. Rather than an unstable loose cannon who often fails due to a tendency to shoot himself in the foot, he's depicted as intentionally harmless. On occasion Mary Sue has been known to help Zim on his mission to conquer the Earth.
Many fans also think GIR is CUTE. The writers made the episode "GIR Goes Crazy and Stuff", which reveals GIR's evil side. In this episode, among other things, GIR tries to KILL ZIM. Jhonen Vasquez hoped that the episode would make people "uncomfortable" with the robot. It didn't work.
Misaimed Marketing: See Misaimed Fandom. GIR's "cuteness" has been exploited in every conceivable way for merchandise. Most of the merchandise is of GIR. (Not to mention Jhonen gets no royalties for it anyways.) Lots of people were introduced to this show through Hot Topic, and if you ask them what they like about Invader Zim, they will tell you one of the following:
A) They haven't watched it
B) They like GIR!
C) Who is "Zim"?
D) All of the above
Moral Event Horizon: Zim's attempted murder of Dib in "Bad, Bad Rubber Piggy" does it for some. It's not really the worst behavior he's ever demonstrated, but the rapt, gleefully anticipatory look on his face as he watches the life go out of Dib's eyes -- with accompanying flatline beep -- is creepy on a personal level that he doesn't often reach. And how does Zim react to Dib's death? Summon a grape soda and go about his day as though he just got home from the office and wants some personal relaxation.
Others can say when in Hobo 13, Zim sacrificed everyone on his team to advance himself to the fortress of pain.
In "Game Slave 2", Gaz may have crossed this when she attempted to throw Iggins down an elevator and kill him, for stealing her Game Slave 2. Mind, thanks to Executive Meddling he wound up surviving, and was almost an Asshole Victim in the first place, so perhaps this lessens it.
Or possibly in "Dibship Rising", when she used a device to try wiping out all mankind.
In the DVD commentary it's stated that "GIR Goes Crazy and Stuff" was deliberately intended to induce this and make people "uncomfortable" with GIR -- the common perception of the robot as good-natured and kind wasn't what Jhonen had hoped to portray.
Moe: The whole reason why GIR is loved to the point where Zim Fans are starting to get sick of it.
Zim, despite the fact that he's trying to destroy the world and stuff, can be this. Especially since he sucks at his "job". Then there was him as a Smeet...
Next to GIR, Dib is probably the most Moe character. He's just so Adorkable, not to mention he's a huge Woobie.
Dib: Wait, Zim! Promise me you're on our side this time.
Zim: I know not of sides, Earth Stink, but just this once I agree with you. The hamster must be stopped.
Nausea Fuel: "Career Day", "Rise of the Zit-Boy", "Dark Harvest", the turkey dude's lucky neck meats in "The Sad, Sad Tale of Chickenfoot"... speaking of which, the scene where a guy's eating soggy french fries out of a tub full of dirty dishwater grosses out Jhonen himself.
"Halloween Spectacular of Spooky Doom." Just... that. *shudder*
Selfish Good: Dib in the earlier episodes. All he seemed to care about was to capture Zim and prove that aliens are real, before caring about the world more.
Sending Stuff to Save the Show: The fan group Operation Head Pigeon spammed the Nickelodeon executives using phone calls and message boards. The group has prompted a Zim marathon, putting it back on Nicktoons, and a best-of DVD entitled "Operation Doom".
Cargo Ship: Sort of an inversion. GIR seems to have a little crush on Gaz. It's rather subtle though. Evidence for this can be found in the episodes "Bloaty's Pizza Hog" and "Tak, the Hideous New Girl".
Foe Yay Shipping: The most common (by far) pairing you will find is Zim/Dib. For many it's pure Squick, but it's undeniably popular.
Idiosyncratic Ship Naming: Takes the form "_A_R" (for "X and Y romance"), with the blanks filled in by the first letters of the characters' names (e.g. ZADR from "Zim and Dib romance"). Made somewhat problematic by the fact that several characters' names start with the same letter.
Ugly Cute: While many fans identify some of the characters as this, Jhonen Vasquez expressed his disdain for GIR being called "cute", because GIR isn't supposed to be cute (just funny).
Unintentional Period Piece: Oddly enough since the show is set Twenty Minutes Into the Future. Though they are hover drones, video stores are still very popular, as are big clunky computers, and there doesn't appear to be any cellphones on Earth which all mark the show as a product of the early 2000s.
"Speaking of Dib, I’m shocked at just how many girls like dressing up as Dib. Seriously, I saw a dozen female Dibs this weekend, and barely one male one. It seems like Dib has almost become some kind of butch-girl icon. I think that’s pretty cool. "
Villain Decay: Whether you consider Zim or Dib the villain, they both got considerably worse at their tasks as the series advanced; early episodes would usually have one best the other, while later many ended with them both of them enduring some terrible trauma.