Given the large number of variations on the same stories, there's quite a bit of this within the spinoff comics as well. One of the more common interpretations in runs of the first gen and its remakes is the common Fanon theory of Blue/Gary being Oak's Unfavorite while his grandfather favors the MC appears quite often. Other runs paint him as a flat-out Jerkass, while others split the difference for a Jerkass Woobie.
Another frequent point of variation: how gym leaders and other trainers respond to death on the battlefield. Any given gym leader could be portrayed as a professional who has accepted death as a natural consequence of battle, a friendly foe who's honestly shocked at seeing their opponent's pokemon die, or an utter Jerkass who gloats and rubs the loss in their face.
Also in Hoenn runs, Wallace tends to be depicted as Camp Straight and in a relationship with Winnona. This is probably influenced by Pokémon Special.
Common Knowledge: The original challenge did not have "No Legendaries" as a rule (Legendaries weren't caught simply because they weren't the first encounter Nuzlocke ran into in their area), nor was "Blackout/Whiteout = Game Over" part of the original rules. ( Ruby ended the way it did probably because the author felt turning the loss against the Champion into a Downer Ending worked well from a story perspective) In fact, "you must nickname all your Pokemon" is generally accepted as part of the core Nuzlocke rules these days, but even that wasn't the case in the original either. The only two rules the first challenge used were stated in the first panel: "Release a Pokemon if it faints" and "Have to catch the first Pokemon on each route and nothing else".
Complacent Gaming Syndrome: Plagued with it to a degree. Despite the random nature of the game and how death can result in some odd teams, a lot of the comic makers tend to make similar choices of starter Pokemon and likely make similar choices on keeping mons if they are able to use them. A Johto locke that picks Chikorita tends up attract intrigue and curiosity since it is a rare occurrence while a Sinnoh locke that picks a Chimchar is regarded as another run-of-the-mill Nuzlocke.
And most people are almost always going to get, the bug type, the rodent, the bird, and a zubat at some point. Just cause of how common they are.
A LOT of Nuzlockers seem to have waifu-time with their favorite Gym Leaders. Or, more recently, with N. Here's actually a few Nuzlockers who shipped rivals with Gym Leaders.
Or, if there's more than one rival (like in Ruby and Sapphire, Diamond and Pearl, Black and White, and X and Y), rivals with each other. Kynim's Diamond Nuzlocke is a noteworthy case of this, as one of the endgame pairings is the two male rivals.
Misaimed Fandom: The Nuzlocke challenge itself qualifies—the creator of Pokemon stated that he wanted the Non-Lethal K.O. system in there partly so that the game doesn't become impossible and partly because he didn't want children to grow up associating death with losing a game. Didn't stop this self-imposed challenge from becoming a thing.
Rescued from the Scrappy Heap: A pretty normal occurrence in Nuzlocke runs. Due to the rules, players often end up having to use Pokemon they don't normally use, and consequently develop newfound respect and appreciation for them.
"Stop Having Fun" Guys: It is to be expected, given it is part of the Pokemon fandom, albeit rare. There are some who take the challenge rather seriously and will criticize the teambuilding of other players (if they are sharing the progress and results of their challenge) even though one of the premises of the challenge involves adapting to having no choice on what mons you can use outside of ones given as gifts.
Strawman Has a Point: There's something to be said for N's claims — that Pokemon battles are cruel, selfish, and only result in Pokemon being hurt — on a normal playthrough. On a Nuzlocke run, he's pretty much right.
The Woobie: Chances are you will come across a character who has suffered so many hardships, be it the loss of a friend, a crushing defeat, or even personal matters, that you can't help but want to hold them and comfort them.
Several of the gym leaders, but Erika as a pot head takes the cake.
N in White: Hard Mode is much worse than Canon; he's willing to kill Pokemon just to lecture their owners about how "this wouldn't have happened if you hadn't caught them!"
Also in White: Hard Mode, Cheren and Bianca being creepy psychopathic manchildren who stalked and hounded Hilbert so badly that he hung himself just to get away from them—and their reaction to seeing this is simply mild disappointment (with the mildly unsettling implication that this has happened before).
Mewtwo goes the exact opposite direction of how most fanworks, Nuzlocke or otherwise, portray him. In the games, Mewtwo had very little personality, but the 'dex and most hints from its backstory portray it as an easily angered Blood Knight that takes no greater joy in anything but fighting. The anime popularized a more tragic portrayal of the character, a broken creature that sees itself as an abomination and bitterly hates humanity for making it that way, whilst simultaneously having a cold calculating mind. "Fire Red: Hard Mode" portrays a horrifying merger of the two characterizations, with a highly intelligent and manipulative Mewtwo who not only bitterly hates humanity, but also wants to destroy them, and displays a sadistic love of killing both humans and Pokemon alike.
Broken Base: Episode 8 of White: Hard Mode has been getting this for having Ruby catch Victini, showing the "No Legendaries" rule is not in effect, resulting in either people okay with it (mostly due to the mon's personality) or crying "ruined".
Although to be fair, the original comic never has never had the "No Legendaries" rule. The reason he didn't catch all the legendaries previously is because they weren't the first Pokemon he encountered in an area. Victini was.
Growing the Beard: The Ruby run was good, but rough around the edges. The Fire Red run saw a general improvement in the art, dialogue, characterization and plot, and was an even better series.
And it seems like the White arc is starting to grow it even further, by having it in full color, the art being a lot more clean, and not overusing the Lost references.
Harsher in Hindsight: Meta-example. On late Feb 2017, the author would had his car broken into and have his 3DS and all his Pokémon games stolen. This meant that that he lost all of his friends in real life whether they lived through the story or not, meaning that in a way, they died for real. The only legacy left of them would be the webcomic itself where he already written down the notes for White.
Jerkass Woobie: Ruby is by no means a total jerk, and he warms up to any Pokemon he initially hates, but he's often a bit cynical in some chapters. You'd be too if your own father favored a Slakoth over you, you watched several Pokemon die, lost all your remaining teammates against the champion, almost lost everyone against another, were used by an all-powerful legendary who proceeded to kill another party member, and flung three years into the future in the aftermath without the remaining one of your Pokemon, where the cycle starts again via a certain green-haired Pokemon rights activist. Guy's got it rough...
Blastoise also counts to an extent after all the crap he took from Gary despite being a repeated Hero Killer for Meowth and Blamo. As such, his The Dog Bites Back moment feels all the more cathartic.
Surprisingly enough, Ghetsis is this as of episode 11.
Harsher in Hindsight: In Hale's comic, Hale tells May that she should kill herself. Guess what she tries to do later on.
Hilarious in Hindsight: This◊ strip has Hale hitting his Slugma and burning his hand as a throwaway gag. Fast-forward to Pokemon Xand Y, and playing with Slugma in Pokemon Amie results in the same thing.
Fridge Brilliance: Giovanni is startled when Candace disguised as a Rocket greets him with "Hail Giovanni!", because he's not the leader of Team Rocket any more. She blew her cover.
Moral Event Horizon: Candace breaking and entering into the Olivine Town lighthouse, now a shrine to honor Jasmine who sacrificed herself to allow the rest of the town to survive, by way of Forretress' Mirror Shot to get the badge, considered a sacred object by the survivors, was viewed as this by some people.
Nyachan's Nuzlocke Challenges:
Ship-to-Ship Combat: So much in her Pearl run, between Lily/Gary and Lily/Kess, that she had to threaten to holler at the mods in the opening post of her Sapphire run. Gary won, if you're interested, but Word of God says the author originally intended Lily to end up with Kess before doing a total 180, which was probably the cause of this.
Lyrax's Gold Run:
Moral Event Horizon: Lyrax's Gold run immediately establishes the rival as irredeemable when he steals both of the leftover starters, apparently just so he could tell Lyrax "Don't follow me or I'll kill one of them." He does.
In Azza's Run:
Moral Event Horizon: Charmeleon (and his trainer as well) make it clear they're well over the line when Raticate argues that the murder of innocent Pokemon was completely unnecessary, and demands to be released from the team. They do so, but then Charmeleon claims that since Raticate is now a wild Pokemon, he can do whatever he wants, and very brutally murders Raticate as well.
Silver as just a nice guy everyone hates for no reason. He noticed Elm drop a starter's Pokeball and tried to give it back, Elm accused him of stealing, and he fled.
Moral Event Horizon: Kit considers Kyogre killing his Grumpig to be this, even nicknaming the legendary "Murderer"
Baskerville manipulating Fortune into hugging her in frount of Lyra, after finding out Lyra had a crush on him, was probably the point she earned her Scrappy status below. She's killed off pretty soon after, only expressing remorse for doing this when she's about to die.
Nightmare Fuel: The Black run, due to it being the interpretation of the glitchiness that occurred when the author used cheats to sequence break in the game.
The Scrappy: Baskerville. Initially she seemed like a well-meaning jerk, but later she was proven to be pure jerk. She did get a bit of an Alas, Poor Scrappy moment when she died though.
Broccoli and Bottles' deaths were as horrifying as they were heartbreaking.
The nightmare Jet has just before her battle with Lenora—if the savage looking Watchog and Herdierseating Firedog, Lilly and Leer don't scare you, than the downright demonic looking version of Lenora looming over them and laughing maniacally will. And then Broccoli and Bottle's ghosts show up...
Nightmare Fuel The Unnamed Protagonist from Pitch Black is a terrifying, evil, sadistic protagonist. From the beginning it's established that he's NOT a good character, (Considering we see his first activities IMPALING POKEMON ON HIS PICKET FENCE). From then on, any Pokemon he catches he forces to fight and brutally murder his friends and family and sees them nothing more as tools, even going as far as to KILL his own Pokemon. Basically, he's an even worse version of Paul. His Oshawott, Icarus, MAY be just as bad.