Batman is Badass Normal. Already he's fulfilling the realistic wish of so many. We know we can't fly or aren't super strong or super fast. Batman though is a hero that supposedly, "could be you or me." (from Batman: Unmasked) He's our projection of accepting our limitations, but still reveling in how far we can take it.
Second, Batman has the whole Dark Is Not Evil and Good Is Not Nice bent going for it. Mankind longs to be good, but at the same time we applaud the swift and brutal defeats of those in the wrong. Batman does both of these things, and yet still remains a good guy for not crossing the Thou Shalt Not Kill line in modern times.
Third, Batman is the paragon for our love of cunning and intelligence. True, he doesn't exactly have an alien encyclopedia, but the notion of being Crazy-Prepared for the future in the chaos of real life is extremely appealing, and Batman can somehow do it without seeming silly or having fans screaming Ass Pull.
Fourth, Batman is our selves rising above reality. Batman lost his parents at a young age, but sought to go forth and create a new order no matter the personal cost. This is extremely admirable as not only has he moved forward to higher causes, but he's doing it in a manner that we enjoy watching. (Heck, his charitable work as Bruce Wayne is practically a footnote compared to what Batman has done, but perhaps that's just the way comics work)
Fifth, Batman operates in a Crapsack World in order to better perfect it as his old home. Sure, we might put on airs to help save the world, but Batman is going out and making a truly depressing world better, and his Tragic Dream is something many admire.
Batman is generally considered to have one of the best, if not THE best, Rogues Gallery in comic books. Part of the success of Batman, and part of the contribution to his legendary status, is that his Rogue's Gallery is such a perfect shattered reflection of Batman himself.
- The Joker: He represents the chaos and dark impulses that Batman struggles against every day — in crimefighting and within his own mind. Newer iterations have also played up his Determinator attribute to contrast with Batman's. While Batman will never stop trying to stop crime, the Joker will never stop trying to get Batman to break his one rule.
- Two-Face: Represents the struggle between dual identities inherent in Batman/Bruce Wayne's psychology. Harvey's own Hero Complex of having things be fair so much that he creates his own villian/nemesis in Two-Face just for balance and duality. Further, his coin-flipping gimmick - leaving his actions up to random chance - largely represents a rejection of the entire concept of moral responsibility. This concept utterly *defines* Batman (and many other heroes and villains).
- Riddler: His obsessive-compulsive and self-sabotaging traits reflect back the obsessive and possibly self-destructive side to Batman's own personality. His championing of intellect to commit crimes also reflects Batman's detective abilities and his use of intellect to solve them.
- Scarecrow: His main tactic is to rule through fear — similar to how Batman cultivates a frightening persona to intimidate crooks and hoodlums. Also their costumes are foils in that Scarecrow had a fear of crows so therefore he dressed up a Scarecrow make himself feel strong meanwhile Batman had a fear of bats but ended up over coming it by being his fear and dressing up as it to frighten his enemies.
- Penguin: Penguin acts as a rich socialite, while actually acting as a crime lord or black market smuggler. Similar to how "Bruce Wayne" is an act for Batman, only he does so as a Rich Idiot With No Day Job while also acting in philanthropy rather than descending into criminality.
- Man-Bat: This is the danger the Batman has if he errs too far on the side of being the Bat without remembering the man.
- Catwoman: Uses an animal motif to get what she wants, and is highly athletic in using said motif. Also, both rose from personal tragedy. Their similarities and the Dating Catwoman part of this contrast make both very strong foils to each other, particularly in the fact that Batman keeps trying to reform her. Also, just as Batman is an unpowered (albeit highly skilled and trained) human who operates alongside people granted godlike superpowers, Catwoman is essentially a professional thief with an animal gimmick who nevertheless manages to hold her own against megalomaniacal gangsters and psychotic maniacs.
- Poison Ivy: Like Batman, Ivy fights for what is ostensibly a noble and socially admirable cause involving protecting those who cannot protect themselves. However, Ivy becomes a Knight Templar who identifies too much with her cause and cannot see past it to the point where she ends up causing just as much if not more suffering than she prevents. She is what Batman can become if he identifies too closely with his abstract cause and forgets that the people he fights against are still people.
- Mr. Freeze: In his more modern incarnations at least, has suffered the brutal loss of a loved one that has subsequently defined his life in the same way that Bruce Wayne losing his parents defined his. In some incarnations, he also shares Batman's Awesome by Analysis abilities.
- Bane: Bane is a Cultured Badass, and a Genius Bruiser, traits he shares with Batman. Furthermore, both he and Bruce Wayne grew up in environments that challenged them to become the best just to survive. The difference is that Bruce Wayne went to these places on purpose, while Bane was born in a hellish prison, and had to escape. On a personal level, Bane is defined by his venom use, and his ruthlessness, making him a counterpoint to Batman's defining traits: Badass Normal, and Thou Shalt Not Kill.
- Hush: Many of Batman's villains have a personal tragedy for a backstory, but none echo Bruce Wayne's own so much as that of Thomas Elliot. He grew up in the same social circle as Bruce Wayne, and showed a promising intellect at a young age. But Hush hated his abusive parents, making him a possible version of Batman that would have arisen if Thomas and Martha Wayne's parenting had gone horribly, irrevocably wrong. He also often fails in schemes because despite the penchant for using people that he and Batman both share, Hush doesn't understand the concept of friendship, while Batman, for all his faults, has been saved more than once by the fact that he cultivates real relationships with the people around him. As icing on the Shadow Archetype-cake, he's also performed extensive facial surgery on himself to look like Bruce Wayne, a grisly imitation of Bruce's Master of Disguise traits, plus the fact that his 'Bruce Wayne' persona is ultimately a false one.
- Ra's al Ghul: Ra's exists in the shadows, using his resources, servants, intellect, ability to manipulate others, and physical strength to impose his personal morality upon the world. He's even been known to take young apprentices, and cultivates a borderline religious image of himself as a way of controlling those around him. Further, part of his motive is that he earnestly believes that life is precious, but that people mistreat other living things. Unlike Bruce, Ra's is willing to kill to protect 'life' in a general sense. In a way, he's every one of Batman's traits perverted for evil. Interestingly, Ra's seems to be aware of this in some capacity, as he often tries to recruit Batman as his successor.
- Hugo Strange: Both are trying to understand the mind of a criminal in order to reach a goal.
- Mad Hatter: Uses mind control devices to live in his fantasy world while Batman faces reality.
- Black Mask: Both try to run the family business, only for Black Mask to fail and decides to go into crime. Further, Black Mask at one point ended up having his trademark black mask fused to his face in a fire...echoing how Bruce Wayne can sometimes define his own worth by how he does as Batman.
- Maximilian "Maxie" Zeus: At least in The Batman, A wealthy businessman who uses his money for gadgets and for ruling over Gotham.
- Alternatively, Batman has built up a reputation in Gotham after years of fighting crime, to the point where people identify him so much with Gotham that during the time between Batman's death at the hands of Darkseid and his return, "Batman" Jones says that without Batman Gotham "has no one to answer to. [Gotham has] lost its god." In both the DCU and our world, Batman has a cult status, similar to a god. Maxie Zeus on the other hand, models himself after a preexisting god and believes himself to be one while Batman remains aware that in spite of his status he is fully human and not godlike, at least not in the sense that Zeus believes himself to be. Both characters are about myth and legend: Batman became a legend - one that never existed previously - through his persistence and hard work while remaining aware that he is not a god, while Maxie Zeus suffers from delusions of grandeur and immediately started declaring himself to be Zeus. Essentially it boils down to these elements: Both are rich and deluded to some degree about what they can do with their influence; but Batman has been more successful in becoming Gotham's "god" through years of his own hard work while Maxie's success is all in his head. Alternatively, you could interpret them both as not gods, but idols, with Batman being the genuine article who deserves it while Maxie is a false idol.
- The Ventriloquist: Similar to Two-Face's dual personalities but unlike Two-Face and Batman, Wesker's other persona subconsciously goes into his puppet which Wesker possibly doesn't know its him making the threats towards himself and others.
- Victor Zsasz: Both lost their wealthy parents and wants to save Gotham, only for Bruce to use the wealth to help others and to use it against crime while Zsasz lost his family's wealth due to gambling and believes saving Gotham by murdering every citizen so he can "free" them from their "prisons".
The analysis can go even further, in that like Batman himself many of Batman's enemies have either ostensibly sympathetic back-stories or some inciting incident in their past that motivates their actions, just as the murder of Bruce Wayne's parents is the primary motivation for his actions as Batman. However, where Batman uses this incident as a motivation for trying to make himself and the society he lives in better and to prevent what happened to him from happening to other innocents, his enemies have all succumbed to despair and madness, and instead use their traumas and pain as an excuse to lash out and hurt others.
The entire comic series can be interpreted as a representation of the failure of conventional morality from a quasi-Nietzchean perspective. Philosophically speaking, Gotham City is a representation of everything that could possibly go wrong in a modern urban landscape. The system has broken down to a nightmarish degree. Corruption is rampant at every level of government. Street crime and urban blight are so prevalent that they're just considered part of everyday life. Even the most outwardly decent individual is just one traumatic experience from transforming into a baroque Serial Killer. The conventional forces for Law and order consistently fail to address the problems of the society they were created to serve, which necessitates the appearance of a non-conventional force (ie. a vigilante who makes extensive use of psychological warfare and theatrics, rather than logic and procedure). Modern society's problems have grown too large and too complex for its traditional ethics to address. Something new must be created to deal with these problems.
Which brings us to The Joker. He is the extreme of criminal behavior that law is unable to resolve. A constant throughout the series is that Joker can not be redeemed. His madness cannot be treated or cured. In fact his madness is slightly contagious; trying to analyze him, or in some cases just spending a significant amount of time in his proximity, may drive you mad as well. He can't be contained either; imprison him and he'll just break out again. Only one thing can really be done with him...and no representative of law and order - not even Gotham's extraordinary agent of it - is willing or able to do that. Thou Shalt Not Kill is the one rule that no one will break, even though it will quite handily solve the unsolvable problem of the Joker, and that is presented to us as a good thing. Unfortunately traditional concepts of "good" and "evil" do not apply in a place like Gotham. The Joker's continued existence - and the continued reign of terror he engages in - is the inevitable end product of the moral myopia/moral hypocrisy of Gotham City. Everyone in Gotham - including the vigilante who is technically outside the system - is applying a system of morality to a situation where it is no longer relevant, and in the process contributing to their own self-destruction.
- Poison Ivy and Croc are probably held at Arkham just because a normal prison couldn't make the accommodations necessary to house a giant lizard man and a woman who controls plants. Not that Arkham does a great job either ...
- I dunno, they probably qualify for a fictional psychosis relating to psychological association of one's identity with the source of metahuman traits rather than human society. We probably don't have a formal psychological disorder classification for people who categorize themselves as plants and crocodiles rather than humans, but a world with rampant metahumans probably does. They're probably sent to Arkham because their crimes could be stopped (or at least reduced) by convincing them to think of themselves as Homo sapiens, which can only be done at a psychological facility.
- "We probably don't have a formal psychological disorder classification for people who categorize themselves as plants and crocodiles rather than humans"? I feel like this needs a "yet", seeing as we have those people now.
- Its been said that KC has been suffering from his mutation/disease so much that he acts more like a reptile than a man.
- The conditions that you are all looking for is called Species Dysphoria and Clinical Lycanthropy. It's a condition that frequently contributes to the more extreme immersion in abhuman identities frequently found amongst subcultures like the Sanguinarians and Furries.
- Clayface and Man-Bat probably suffer from a similar "no longer thinks of himself as human, and thus not bound by human social rules due to abnormal metahuman morphology" disorder, emphasized by how Man-Bat is usually a villain to one degree or another, whereas Kirk Langstrom isn't (there's probably some identity disassociation going on there too for Langstrom)
- Scarecrow's characterization varies rather widely, but Jeph Loeb's characterization leaves the impression that he has Dissociative Identity Disorder - when his mask is ripped off in Hush he begins speaking in a normal tone (when he had been singing "Hush little baby ..." before), and doesn't seem to answer to "Scarecrow" and "Jonathan Crane" at the same time. Other characterizations are open to a litany of "diagnoses." Of course, see the "Dr. Crane is faking it" entry above for Alternative Character Interpretation.
- The Mad Hatter is said to be schizophrenic.
- Harley is all kinds of crazy, but we can probably specifically pinpoint some variation of Stockholme Syndrome or patient-doctor transference, at least in her Start of Darkness.
- Calendar Man is almost certainly obsessive compulsive to some degree or another what with his inexplicable calendar theme.
- Firefly is a pyromaniac, and that's a legitimate type of impulse control disorder.
- Maxie Zeus is literally and explicitly delusional.
- Ra's al Ghul is occasionally cited as suffering from a type of insanity induced by the side-effects of the Lazarus pits having more lasting effects on him due to repeated use; they may be hoping that therapy can counteract this and make him a little more rational in his ecological aims.
- Joe Chill: Alcoholism
- The Joker seems to have multiple disorders instead of just one:
- Anti-social personality disorder-He sees others are part of an elaborate joke.
- Dementia-The Joker's whole worldview, plus the fact he considers the world he inhabits fictional.
- Depression-The Killing Joke implies that the Joker uses insanity as an escape from pain.
- Dissociative personality disorder-The numerous personalities the Joker has adopted over the years.
- Erotomania-The Joker is obsessed with Batman as his arch-enemy, often refusing to kill him to continue their rivalry. It borders on outright romance in the most twisted way possible.
- Narcissim-Sees his crimes as one big game, and loves to goad others(mainly Batman) into playing it.
- Sadistic personality disorder-The Joker's favourite crimes are hurting his foes on a personal level, and much of what he does is basically artistic sadism.
- Sociopathy-The Joker is incapable of empathy or guilt, highly intelligent and good at manipulating others. If you take the interpretation that he's faking madness.