These are a lot more common in freeform rps, but it's some lovely lingo I learned from a particular chatroom, so I really wanna spread it around.
The Hindu God Avenger Squad: When all or most of your characters are absolute superheroes and can't possibly be reasonably challenged by the lower-level adventure you had in mind. Ideally superhero characters are the natural endpoint for most progression system-based RPGs, but the HGAS has a little extra turd-flavoring sprinkled over it. These characters will all be early teen wet dreams. Expect lots of anime reference pictures, Latin names, etc.
If they're overly masculine, expect them to be movie vikings, all over 30 years old, still sexually attractive, scarred to shit despite being good at fighting and trained in nonlethal circumstances, and sporting names using lots of "K" "R" and hard "G" souns. Kargan, Varg, Grak, etc. because those are the "badass" letters. Young men of the more weebish persuasion will dual-wield katanas, (or wield just one japanese weapon at a time, if they are self aware enough to realize that this is ridiculous, but not otherwise aware enough to know /why/.) are often shirtless and impossibly strong despite being weedy by the standards of the other male characters and sometimes even the women, and will invariably have some sort of "quirk" wherein they are given a propensity to do things that any person would consider perverted, autistic, or downright sociopathic in real life. Expect them to be extremist and overly dedicated to certain menial things even in their downtime to emphasize their "quirkiness" and "discipline", which under any other circumstance would just be called out as the unhealthy obsession of a weaponized sperg. Expect Edgelords to be literally Sauron, or some other extra-grimdark or even more combat-focussed interpretation.
Expect women to be beautiful, late teenaged warrior-mages with unnatural and/or heterochromic eye colors and fantasy or arthurian names that are never less than three syllables. They will always seek the Lawful Good moral high ground, and attempt to philosophically call out the other characters when they behave in a way that breaks their MLP fairy-tale morality. When confronted with a difficult situation or moral choice where right answers can be hard to find, they will always take the copout and/or try to find a loophole. If forced, they'll assume both answers are moral equivalents without thinking and experience DEEP SADNESS about it.
Since all of the characters will inevitably be horrible at relationships, this sadness will go nowhere, no one will react to her emotional displays because they consider her to be a smug magical girl bitch anyway, and she will often be accused of playing the lone-wolf edgelord if she doesn't eventually get bored and give up the emotional trauma she's suffered never to mention it again until the next time she receives it.
Expect these roleplayers to rest on laurels they don't actually have and believe that the coolness of their character is a given trait rather than an earned one. Expect all or most dialogue to be snappy, psuedo-philosophical, and overly moody so that they can fill their profiles up with the quotes of their fictional characters to appear more deep and experienced than they are. Also expect everyone who thinks they're funny to play an absolutely painful comic relief character, who will immediately whiplash into being serious or even downright melancholic in a grim situation when his team morale might actually benefit from at least a passing joke. Expect everyone who takes themselves seriously or acts cynical to never change, ever.
Expect characters with mortal wounds to bleed at least 500 words of "inspiring" manifesto instead of regular blood. Expect them to take cues from Legend of Korra and always be mentally indomitable hardasses who never give up, always win because they're the good guys, always overcharge their bodies/powers without lasting consequence, and never have anything resembling a character arc. H-G-A-S. What does that spell? HILARITY!... Or the Death of Fun, depending on whether you're a reader or a GM/fellow player.
If you want to know what a HGAS looks like and don't have enough literate middle schoolers to put one together, the Suicide Squad movie provides an eerily accurate example. You can practically hear the irrhythmic typing of the half-pubescents behind every ridiculous interaction.
The Noir Marine: The Noir Marine is like the Reasonable Marine in Warhammer. Except they're very boring, overly technical, and generally about as dry to read as a dictionary. So basically all the people that construct an army of Reasonable Marines in Warhammer. Army brats or just Arma Brats who always play dark, angsty mercernaries, worship "realism" and attempt to be the badass normal or batmans of the group, especially if they've been incorporated into a game that's fast becoming the adventures of the HGAS... But by virtue of their own Mythbusters code of honor, they can't allow themselves to use weapons that aren't real, or be as insanely overpowered as the others even though they try their damnedest. They may become an HGAS of their own in a game where only humans/realistic things are allowed, and lord a character's "inacurrate" or "impractical" nature over any player that hasn't similarly minmaxed their character according to the perceived limits of the human race.
Expect lots of internal monologues about war, and how war never changes. Expect all characters to suffer from mental illness and PTSD as a manner of convenience, and expect them to be very jaded and contemptuous elites with a chip on either shoulder, but ready to very emotionally die for their "Friends" as soon as the GM decides to clue in the players that a climax might be happening right now.
With the rise of the Skallagrim Grognards and the growing popularity of gritty fantasy, you can also find plenty of Noir Marines in fantasy or medieval settings, each trying to out-practical the other. They will more or less always try to emulate things like Game of Thrones, Berserk, and the gorier "realism" parts of the Warhammer Fantasy setting/rpg, no matter what feeling or gameplay the setting is attempting to evoke.
The Wizard of Space and Time: Their name may be different, their character sheet may be changed to fit the mold, but the Wizard travels through all settings and time periods more or less untouched by the constrictions of the world around them. The Wizard is a perfect individual, an idealized version of, no doubt, the author. And despite being so heavily based on a person from the real world, they will have a negligible reaction to even the most extraordinary of occurences. If it is especially strange or surreal, expect them to do the "Silent Eye-widening" reaction of a character who is clearly too cool and too serious for this silliness. (If you don't know what this looks like, check out any amateur anime, sonic, or pokemon OC fan animations, the apparent originators of this cancerous living emoji expression.) They aren't necessarily super powerful, and don't cause HGASes when they group together... But quite often, habitual HGASsers will have one or more Wizardly characters to go with them.
The Godzilla: If your game is to be about barebones survival, guerilla warfare, horror, mystery-solving, politics, or just a peaceful slice of life, expect The Godzilla to be an absolute (sometimes literal) beast specialized in raiding for supplies, open combat, horror-slaying, war-fighting, and brawling, and expect them to be constantly trying to instigate those aforementioned things. The Godzilla is the orphan high schooler whose father regularly gave him commando training and mastery of the family blade before somebody promptly mass-assassinated their family. Presumably to keep the weebs from laying more eggs. The Godzilla is the bulletproof scorpion centaur with Deadpool healing and acid blood in the Mass Effect squad. The Godzilla is the giant "genetically modified" hyperintelligent Deathclaw Legendary who hangs out with a group of regular survivors for some reason and randomly kills some of them.
They will often be ridiculously powerful/good at what they're doing, and call YOU a godmodder if you claim to survive, escape, block, or in any way negate anything they're doing. They're usually in the minority, but 3 or more in an rp with a lot of players can create a Hindu God Avenger Confederacy as a separate "subset" of the plot. This term is inspired by the aforementioned invincible Deathclaw, whose character and the characters of his HGAS clique were sort of Wizards of Space and Time all their own, from an rp that the "survivors" posthumously nicknamed "A Boy and his Dogzilla", which later morphed into just "Godzilla".
This character appeared in many rps since, but ever since the intelligent members of the original site started ousting him and the other parts of the forum left over started filling with idiot noobs, he left and I only ever saw him once again years later... As the Deathclaw was apparently his default character for scaly fetish cyber shit. Oh how time changes people!
There may or may not be a helluva lot of overlap between people who fit the various descriptions here. There are quite a lot of symptoms, and it is possible to be all of them, in one or any genre!