(Input welcome on whether any of these examples don't fit) [[folder:Anime and Manga]]
The Eternity That You Wish For, despite a painfully accurate portrayal of the effects of PTSD, fails even by Hollywood Psych standards when a chain-smoking doctor tells the main character that he has to still pretend to be dating his old girlfriend who just woke up from a coma and to pretend that three years haven't passed.
The Pandoras in Freezing all need some serious psychological help. But Setellizer really takes the cake. This is rather inexcusable, too, since the Genetics bases are used as military bases and schools, so psychiatric staff should be some of the first people you hire for a base that houses teenagers trained to fight Novas.
Full Metal Panic!: The Second Raid: Without forewarning, the protagonist is pulled off a mission he has held for six months, involving protecting someone he deeply cares about, with orders to cut all contact and ties immediately and irrevocably. Apparently no-one in his military unit thinks a psychological debriefing would be in order at this point, especially considering how the protagonist is the only person in the unit who can pilot their Black Box mecha, whose super powers are activated by the pilot's ability to concentrate. He is instead belittled by Tessa, his CO, and thrown into a combat zone, where he unsurprisingly suffers a Heroic BSOD.
Nina badly needs help she doesn't get, despite being in the military which should know better. She tried to nuke Tokyo along with her school, and she worked on building another, which turned out a success, much to the dismay of some 35 million people.. Then there's Suzaku who killed his own father, pretty much destroys his opponents in battle, watched his Love Interest Euphemia die in his arms, and finally, annihilated Tokyo. At the end of the episode, he looks to have really lost it. One might ask how Suzaku and Nina even ended up in the military, and how they're allowed to stay - but then you realize that this is Britannia.
Nunnally, in the spin-off manga Nightmare of Nunnally, proves she needed help and didn't get it when all of her repressed emotions manifest in the form of a giant Super Robot as she goes on to have her revenge on the world.
As Red Garden is set in a modern school in New York, it's a trifle peculiar that the grief counselors haven't been sicced on the whole school, especially the friends of the apparent suicide.
Detective Conan: Characters repeatedly note and lampshade that it can't be normal or healthy for six-year-old Conan to see gruesome murder victims on a regular basis. Ran and Sonoko seem pretty creeped out in chapter 43, which is among other things a dismemberment case, when Conan (who found the body) observes thoughtfully that the victim "was wearing her shoes, even though she was cut up." But no one tries to stop her or even get her counseling.
It's easier to count the number of characters who don't directly cause some kind of complication to a mission because of their personal issues in Simoun.
In the Trigun anime series' backstory, five people are put in charge of directing a big chunk of Earth's population to a suitable planet, apparently without any sort of psychological screening since, out of those original five, one turns out to be a loathsome drunkard, and another has a severe case of Love Makes You Evil. This does not end well.
Alien Nine. Don't let the cheery opening fool you, it's downright horrifying. After the protagonist gets raped, has her symbiotic alien mature way too fast, go berserk and kill all the cute aliens, the only thing the adult responsible for her wellbeing re: symbiotic aliens has to say is "try not to kill this one too". And that's not even going to the fact that she didn't want to have a symbiotic alien to begin with, her class voted her to have one.
The Shibusen academy sends children out into the world to slay former humans who have traveled down the demon path, and witches of unimaginable power. You would think the students would be in need of therapy for completing their assigned tasks, but they treat it like killing is no problem.
When Crona, whose mother was trying to create a Tyke Bomb through a program of systematic child abuse, defected to Shibusen, what did they do? Assign a bedroom in the dungeon, far away from the other students, where Crona spends almost every waking moment outside class alone with abusive, sociopathic Equippable Ally Ragnarok.
Tiger & Bunny's Barnaby witnessed his parents' murder at the age of four, and has been burning with the desire for revenge for 20 years. Despite attending an academy which specializes in training superheroes, he doesn't appear to have received any emotional guidance or counseling to overcome his (rather crippling) psychological trauma -- which occasionally causes him to become uncharacteristically violent and illogical -- a Fatal Flaw for a law enforcement official (of sorts) who frequently doubles as a celebrity. Towards the end of the series it is somewhat justified, though -- what with his trusted mentor turning out to be a Treacherous Advisor with memory-manipulating Psychic Powers which he is not hesitant to use on Barnaby whenever the guy does (or remembers) something "unnecessary"...
At least half of the main cast in Iris Zero suffered some kind of trauma, because of what they saw through Evil Eye. Toru helps them get over it, but he has his own issues, due to being bullied as Un-Sorcerer. Teachersdonít want to get involved and see anything that happens around Irises as Somebody Else's Problem. Apparently, no-one thought it would be a good idea to hire a professional psychologist, even though kids with irises are prone to being traumatized by their own power.
In the TV series of Black★Rock Shooter, the school actually has a psychologist, and the main character visits her often. But it turns out she's actually intentionally cultivating student neuroses in order to create Otherworld spirit beings in order to fight the title character.
You'd think an organization like SHIELD would have the resources to talk Ultimate Hawkeye through the assassination of his entire family before he descends into Death Seeker territory. Then again, he may be more useful that way since he's one of their designated assassins himself.
The mission of Avengers Academy is to mold the students into superheroes before they turn into supervillains but the only psychologist they see is Moonstone whom they visit in prison because she's an evil psychopath. The students do seem to be encouraged to confide in their instructors, but with the idea that since their instructors are also especially troubled Avengers, they are better able to guide them. But the trope applies just as much to the adults. When Tigra realizes that her brutal beating at the hands of the Hood and the public humiliation it caused her are still affecting her, she doesn't see a professional about it, but instead goes on a talk show to get if off her chest.
[[folder: Fan Works]]
Justified in one of Neon Genesis Evangelion's fanfictions. Pilots are specially kept in isolation, because normal relations with other people makes it impossible to pilot Evas (whose minds are totally inhuman). Potential pilots who become friends are sent away, because a) bad things will happen since they have a normal relationship with each other b) there is a threat they may befriend Rei, Asuka and Shinji, causing the whole project to collapse.
Towards the end of Million Dollar Baby, the protagonist is rendered quadriplegic in a boxing match, and later has her leg amputated. She ends up being kept alive via a respirator against her will, and eventually becomes suicidal. First she begs her trainer to euthanize her, and then tries to make herself bleed to death by biting her tongue. Instead of getting her the psychiatric counseling that she obviously freaking needs, the hospital's immediate response is to keep her sedated 24/7 so she can't commit suicide. It...doesn't end well.
Stargate: Jack's superior officer knew of his problems related to his son having killed himself within the last two months, but, rather than mandate counseling, General West went against all logic and protocol and sold him on the job because it was likely to become a suicide mission.
A lot of traumatic events happen at Hogwarts and any Real Life school would long ago have had to hire a permanent counselor. The startling lack of such care has led to many fan works which claim it goes beyond negligence and Dumbledore is actually taking advantage of (or in some cases manipulating) these situations to get other characters to do what he wants.
There was the Shrieking Shack Incident involving Lupin, Black, James Potter, and Snape.
Following Cedricís death, school-wide grief counseling was probably merited and even if that was impossible because of the political climate at the time, thereís no excuse for Cho Chang not being offered help Ė she lost her boyfriend in a way that no one wants to talk about and when she needed grief counseling and didn't get it, she ended up using Harry to feel closer to Cedric.
Never mind Harry himself -- ten years of neglect and abuse (which Dumbledore appears to know about but never bothers to stop), then an adolescence peppered with torture, being nearly murdered, witnessing several murders, etc. Plus a martyr complex.
And Ginny, of course. Apparently, when you are possessed by the evil overlord, not punishing you for what he made you do is already being the best Headmaster in this world.
Also Luna Lovegood. We don't know the details, but when she was nine she saw her mother die and she apparently got no help. Plus, she was continually harassed and bullied for at least her first four years at Hogwarts and was so isolated socially that when Harry and company finally befriended her she painted portraits of them all on her ceiling linked by the word "friends".
In World War Z, the US Army who is shown to have given very careful consideration to the dangers of combat fatigue when retaking the zombie-infested East. The US government also takes great care in treating feral children so that they can (more or less) function in society. But the Russian Army on the other hand... not so much.
In the X-Wing Series, Myn Donos is clearly deeply messed up after losing his whole squadron to a trap. Characters who knew him before remark about how lifeless he is now, and he has a couple of psychotic breaks. But while someone suggests that he see someone, it's never imposed on him, he's never ordered to do it.
In the Med Star Duology there's a 'minder' who fills this role for the overworked doctors and turns out to be The Mole, though one is reluctant and had to be pushed into making appointments. This doctor, a Corellian, says that culturally Corellians prefer to medicate rather than talk these things out. Myn Donos is also Corellian, which might explain a bit.
[[folder:Live Action TV]]
In Star Trek: The Next Generation, several characters at times should have seen a therapist but, even though they had an officially designated one on the crew, there are times Troi is strangely absent.
In "Homeward", Vorin, suffering from shock caused by the complete shattering of his worldview, is left to stew alone in a cabin. He kills himself.
In "The Bonding", the child Jeremy has just lost his mother leaving him orphaned and he's also left alone in a cabin to do nothing but look over pictures of his dead parents. Overlaps with Social Services Does Not Exist; despite there being families on the Enterprise, he's not placed with foster parents.
The Mentalist: Patrick Jane had to be institutionalized after his wife and daughter were murdered, and it took him months to become functional again. He's obviously not had much follow-up therapy, though, given how he becomes increasingly erratic in his methods and manner as the show goes on. Considering his primary reason for consulting with the CBI is to help track down the man who killed his family, one would think that regular therapy would be mandated, though his status as a consultant instead of a regular employee may mean they can't force him to go. And so far he's proven too valuable to dismiss, untreated issues or not.
In Stargate SG-1, Cheyenne Mountain actually does have a psychiatrist, Dr MacKenzie, but the guy only shows up when people have outright psychotic breaks or obvious mental problems such as when Daniel suffers hallucinations in "Legacy" or Teal'c is brainwashed and in both cases, he does little to improve the situation. Whenever someone of the government is trying to discredit the SG-team as unfit for their job, that person invokes the strangeness of their encounters affecting them, or how so many of these encounters have risked compromising them mentally.
The Shield might have turned differently if Shane Vendrell had seen a therapist to talk about Shane's feelings of guilt over the murder of Terry Crowley, seeing as his series-long nervous breakdown/descent into murder-murder-suicide was kickstarted by way of Vic ordering him to repress all feelings of guilt over the murder and demanding he pretend it never happened.
[[folder: Video Games]]
Samus Aran is in desperate need of therapy, as displayed by her innumerable psychoses and disorders in Metroid: Other M (post traumatic stress disorder, dependency issues regarding authority figures despite circumstances necessitating independent action, more survivor's guilt than is typically humanly possible) and, to a lesser extent, the rest of the series. This gets particularly egregrious when a phobia-induced panic attack causes her to pass out during battle, nearly getting her squadmate killed, yet nobody tries to rotate her out of combat.
Played with in Spacetrawler. The I.A. Starbanger does have a Therapy-bot, but he's terrible: his therapy consists solely of telling patients that their feelings are irrational. Eventually, Martina realizes that one of her crew desperately needs treatment for post-traumatic stress disorder, so she replaces Therapy-bot with a qualified therapist.
Darkwing Duck : Gosalyn, after having her parents die and her grandfather murdered, seeing the father-figure she just bonded with apparently die, and being kidnapped and nearly killed twice herself, really should have gotten some therapy rather than being returned to the orphanage like it was business-as-usual and encouraged to "show a prospective parent a little more spirit."
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.