The Maybe Magic, Maybe Mundane aspect of Moon Knight's characterisation. For some fans, he's more interesting if you think he's just a normal man who's got serious Schizophrenia and dissociative identity disorder, and Khonshu is just a hallucination. Others however prefer the idea that he's really possessed by Khonshu and is acting as his avatar. Some writers play up the ambiguous nature while other (such as Warren Ellis and the writers following) instead go with things being explicitly the latter. For some, the former idea makes him a somewhat-positive example of mental illness in comics since while he struggles with it and is quite violent he's still a heroic figure, while others find the 'he's crazy' explanation to be somewhat overplayed by certain writers and see it as essentially Deadpool without the fun.
Complete Monster: Raoul Bushman is a thuggish terrorist, crime lord, rapist, and even dictator who roundly proves himself the worst enemy of the Moon Knight. Once the head of a group of mercenaries Marc Spector was part of, Bushman personally murdered the head of an archaeological dig withholding valuable artifacts from him and promptly had the entire town he was in massacred to follow, leaving Spector for dead upon his revulsion. Dealing in many more crimes afterwards, Bushman returned to glory when he became the dictator of his home country of Burunda in a cruel dictatorship that killed millions, systematically exterminating everyone with AIDS within; killing his own men at the drop of a hat; taking advantage of his country's rich soil by having towns and villages wiped out—regardless if the populace can make it out—to build dope farms; and later slaughtering rebels with aplomb solely to get to Spector. Later trying to force Spector's friends to commit political assassinations to utterly humiliate and break Spector and aiding in an attempt to end the planet, Bushman was later brought back from his eventual death to lobotomize an entire asylum of patients to cause chaos all across the city, smugly admitting nothing matters to him more than seeing Spector broken before him.
In Shadowland, Moon Knight vandalizes his own taxi to get beat up and thrown in the dungeon, just to see where it is and how many people are down there.
In the Brian Michael Bendis series, he takes on Count Nefaria (a Thor-level supervillain) several times and eventually succeeds in removing him as the kingpin of Los Angeles. He does this largely by enacting schemes that would be insane to try and by listening to the voices in his head (granted, those voices are Captain America, Spider-Man, Wolverine, and Echo). Unfortunately, the real Echo was killed in the attempt.
He also allows Count Nefaria to beat the crap out of him in a police station to give the Avengers time to arrive.
In the Warren Ellis series, his craziness has looped itself so that he's now one man (Marc Spector) and four incarnations of Khonshu, including "Mr. Knight" (a dapper white suit), a traditional crime-fighting outfit, and an anti-magic suit with—in Ellis' own words—a Giant Fucking Bird Skull for a helmet.
Dork Age: Despite being a (relatively) obscure character, he's had a few.
Marc Spector: Moon Knight, despite being Moon Knight's longest running book to date at 60 issues, is also one of his most obscure and least referenced for this reason. The book was mired in the worst elements of The Dark Age Of Comicbooks and involved a plot about Marc, Frenchie, and Marc's not-quite-dead brother being decedents of the Knight's Templar and involved in a conspiracy involving two warring groups of immortal demons fighting each other for unclear reasons. Subsequent writers tended to ignore this story entirely.
Brian Michael Bendis's short lived run on the book. Khonshu is suddenly replaced by Marc having visions of Captain America, Spider-Man and Wolverine, Marc trying to mimic other superheroes, and a nonsensical plot involving Ultron's disembodied head that went nowherenote The plot line involving the head was intended to serve as a tie in to Age of Ultron, a Bendis helmed crossover event, but due to the event being postponed to make room for Avengers Vs Xmen any sort of connection the two books might have had would be lost on the reader, so the tie-in material was hastily written out, leaving readers scratching their heads as to the plots inclusion..
Max Bemis's run was already off to a rocky start by merit of following the beloved Ellis and Lemire takes on the character, but the controversial choices that the author made have quickly soured his run to members of the fanbase. Decisions including ignoring Marc's increasingly popular Mr. Knight persona, inexplicably reviving Khonshu despite his defeat being a driving force in the latter half of the previous volume, and providing a Soft Reboot by way of bringing Marlene and Frenchie back into Marc's life despite previous authors making it very clear that they had washed their hands of him because of his dangerous lifestyle and self-destructive behavior. The matter of Marlene and his Jake Lockley identity having a daughter, kept secret from Marc and his other personalities, is something most fans would like to ignore.
Out of all of Moon Knight's personalities/incarnations, the currently most popular seems to be his "Mister Knight" persona due to how freaking cool it looks.
Moon Knight in general could be described as this when compared to the rest of the Marvel Universe. He's far from A-List, but he still has a fanbase who are happy to support his book whenever it gets relaunched, and often approve of his appearances in other series or media.
Gateway Series: The Ellis and Lemire runs for their own reasons. Ellis provided an anthology-like format for the series which allowed it to both be awesome and accessible to new readers without any continuity baggage besides the occasional lip service. Lemire, while embracing the continuity more, also worked to retell (and slightly reinvent) Marc's backstory which also allowed accessibility to new readers who don't know anything about the character.
Growing the Beard: After he stopped battling Werewolf By Night and became his own character.
The ending of the "God And Country" arc in the Benson run, with Moon Knight being forced to kill Carson Knowles to save New York.
Issue 6 of the Warren Ellis run where Black Spectre begins his all-out attack on Moon Knight and proceeds to utterly destroy almost everything Marc throws at him.
Jerkass Woobie: Both Black Spectres. The first one had his life and reputation ruined by his stint as a supervillain than lost his son, driving him insane and sending him on another rampage. The second one is so desperate to be unique and special like Moon Knight he becomes a supervillain.
This eventually ballooned to memetically◊ making Dracula Moon Knight's Arch-Enemy in spite of the two never, if not barely, interacting. Though considering Dracula is a public domain character and part of the Marvel canon, it's not out of the realm of possibility that eventually we'll get to see Moon Knight canonically confronting Dracula and demand his goddamn money.
In general, Moon Knight's reputation for being an insane character has led to edits of panels featuring him replacing his dialogue with Ax-Crazy or Cloudcuckoolander traits.
My Real Daddy: Depends on who you ask. The most commonly cited are Bill Sienkiewicz, Warren Ellis, and Charlie Huston. Chuck Dixon is probably fourth. Jeff Lemire is also a new contender, for bringing back Marc's mental illness after Ellis did away with it, and playing with it to a mind-bending genius level.
Nightmare Fuel: Sun King unveiling his powers for the first time, brutally assaulting a nurse before using his pyrokinesis to burn Ravencroft to the ground.
Never Live It Down: Moon Knight has frequently interacted with other Avengers in relatively lighthearted adventures, and most of his stories are no more violent than any other Marvel superhero, yet the story where he carved off Bushman's face in self-defense is cited by some as the key reason that any adaptation of the character has to be R-rated in nature.
One-Scene Wonder: The gold knife-wielding, purple zoot suit-wearing henchman that Moon Knight briefly fights in issue 5 of Ellis's run.
Rescued from the Scrappy Heap: While never a full-on Scrappy, Moon Knight wallowed in obscurity and uneven writing for years before Warren Ellis came along and completely revamped the character.
Signature Scene: Issue five of Warren Ellis's run, in which Moon Knight steadily goes through an entire building fighting mooks one-by-one to save a little girl from her kidnappers.
Also, issue two of Warren Ellis's run, the fight with the sniper: "I'm not real."
The start of the 2006 run, where Marc has literally hit rock bottom. No friends, no Khonshu, no equipment... just a drunken, drugged up wretch.
They Changed It, Now It Sucks!: Has had this from time to time with different factions of his fandom having less than favorable reactions to certain revamps in his personality and character direction.
A big reason for why the Max Bemis and Jacen Burrows run didn't succeed the way the last two runs did was in large part this. Even while they were Revisiting the Roots and ignoring the popular Soft Reboot runs Ellis and Lemire had written, there was a lot of changes from the older content. Notably, they changed Marc's split personalities' personalities; beforehand, Marc Spector was explicitly the violent and self-destructive one, which made things difficult for Marc since that was his primary alter, while Jake Lockley was a working class rough-around-the-edges Nice Guy who, during a time where he was the primary alter, was depicted as a much more typical hero and The Atoner for Marc's violence. Now for some reason, Jake was explicitly the Anti-Hero personality who had forced Marlene into a loveless relationship after getting her pregnant and never telling Marc, while Marc is written more like The Generic Guy in comparison. It didn't help that the run also gave Marlene serious Chickification, retconning her into a Damsel in Distress who Marc supposedly always had to save, rather than how she had previously been written as an Action SurvivorCombat Pragmatist who regularly pulled off Damsel out of Distress, who was In Love with Your Carnage but aware of how self-destructive it was.
Tough Act to Follow: Max Bemis and Jacen Burrows have quite the challenge due to coming off the heels of Warren Ellis and Jeff Lemire's runs, a difficulty Burrows acknowledges. This is not helped by the fact that they've quietly ignored those previous stories in favor of Revisiting the Roots, even reviving Khonshu, whose death was a major event in Lemire's run.
Being a superhero with multiple secret identities has driven the poor guy into borderline insanity and he's constantly having to resist Khonshu's attempts to twist him into a Knight TemplarBlood Knight. He's considered C-List Fodder by most of the other superheroes and supervillains and is extremely lonely, to the point of begging to be part of the Avengers once (although it should also be noted that he also once literally burned his Avengers membership card). And then Echo got killed which almost sent him hurtling over the Despair Event Horizon. In short: it sucks to be Moon Knight.
Marlene and Frenchie. They stuck with Moon Knight for years despite his fluctuating mental state and suffered through terrifying ordeals before cutting off ties with him. Even worse for Frenchie, as he was actually in love with Marc, but Moon Knight's single-minded dedication to his work and instability meant he was unable to even realise this, never mind ever reciprocate; throughout the Benson run, Frenchie is repeatedly shown to be struggling with suicidal depression, and suffers alone because he doesn't tell anyone about it.
His speech to the second Black Specter sums it up best: