Harold "Harry" Osborn is basically a good person who got dealt a rotten hand in life. Born to industrialist Norman Osborn and his wife Emily, Harry never knew much in the way of love and compassion. Emily died shortly after Harry was born and Norman wasn't much of a father. Norman was both verbally and physically abusive to his son, making it clear that gaining Harry but losing Emily wasn't a fair trade.
Harry grew up angry and took out his anger on fellow college classmate Peter Parker when it seemed that Peter acted superior to his classmates. Once he found out that Peter hadn't intentionally ignored he and his friends, Harry and Peter became friends. Later, they even became room mates. Harry tried dating Mary Jane Watson and when she seemed to reject him, he turned to illegal drugs. He was still going through withdrawal symptoms when he witnessed the battle between the Green Goblin and Spider-Man, where the Goblin was impaled by his own flying device. After Spider-Man left the scene, Harry unmasked the unconscious criminal, and saw the face of his father.
Harry blamed Spider-Man for his father's death, and took over as the second Green Goblin. He later found out that Peter was Spider-Man and vowed to kill his former friend. He attacked both Peter Parker and Spider-Man and was quickly defeated, falling prey to a head injury and amnesia. They remained friends for years to come. Eventually, Harry had married a woman named Liz Allen and had a son, Norman Jr. Soon after, his memories began to return, in the form of hallucinations of his father and friend.
He again tried to kill Peter but couldn't bring himself to deliver the killing blow. He found the ability after taking his father's so called "Green Goblin formula," which gave him super human strength, endurance, intelligence...and insanity. Setting a trap for Peter at the Norman Osborn Foundation, he planted a bomb set to kill both of them. When Mary Jane (now Peter's wife) and Norman Jr. arrived at the building, Harry went back to save them. Mary Jane begged Harry to save Peter, upon learning that he was drugged and still inside with the bomb. Harry went back for Peter, escaping just as the bomb exploded. Unfortunately, a side effect of the enhanced Goblin formula struck Harry down, seemingly killing him. (Spectacular Spider-Man #200)
Later, it was found that Norman (who was still alive and had been in hiding) had arranged for Harry to be taken to Europe to get treatment for his drug addiction. He had never died at all. Harry no longer remembers that Peter is Spider-Man but maintains a hatred of his father and all of the harm he has done to the people around him.
A Desperate Son and a Cold Blooded Father
The very core of Harry's psychiatric problems is the relationship he had with his father. Norman Osborn was the center of Harry's world, even though Harry was nothing but an embarrassment to Norman. Harry was a mediocre student and Norman demanded that he pay more attention to his studies, as school was costing Norman "a small fortune." (Amazing Spider-Man #39) His son's average school performance likely grated at Norman because by Harry's age, Norman was on his way to creating Osborn Industries and rebuilding the family fortune. Later, Harry and Peter talk and Harry says that he and Norman used to be friends, until a few years prior, when Norman began taking out his anger on his son.
According to professors at the University of Connecticut, PARTheory (parental acceptance rejection theory) claims that children everywhere need acceptance from their parents and other important caregivers. Lack of parental acceptance can lead to long lasting personality problems: low self esteem, a negative world view, hostility, aggression (emotional and physical) and emotional instability. The researchers also say "More specifically, beyond a certain point--a point that varies from individual to individual--children and adults who experience significant rejection are likely to feel ever-increasing anger, resentment, and other destructive emotions that may become intensely painful."
Self Destructive Chemical Abuse
As said before, Harry turned to drug use after being rejected by Mary Jane Watson. (Amazing Spider-Man #97) Considering the anger he must have already been carrying around due to years of Norman's abuse towards him, the put downs from MJ must have hit Harry extra hard. He certainly didn't put up much of a fight when the drug dealer approached him on campus. The exact type of drugs that he took are unknown but the dealer told him "this stuff is real new, and it aint easy to come by." I suspect that the drug, which was dangerous in and of itself, may have been hastily manufactured in order to get it on the street as soon as possible. (Just as in any business, dealers want to beat the competition to the punch.) The haste in which the drugs were made may have made them especially dangerous.
Later, Peter notices that Harry "always had a lot of bottles in his medicine chest--pills to keep him up--to relax him--and to put him to sleep." (Amazing Spider-Man #97) Harry seems predisposed to drug use, showing that he may have an addictive personality. Individuals with these personalities often show impulsive behavior, weak commitment to the goals of society, a sense of social alienation and heightened stress. Harry didn't try to walk away from the dealer (impulsive behavior), wasn't interested in running Osborn Industries despite his father's demands (weak commitment to goals) and suffered from social alienation (from his father, to Mary Jane to arguments he had with Peter).
He was also impulsive in taking the Goblin formula. He knew full well that Norman was the Green Goblin and that he had killed his friend, Gwen Stacy. It must have occurred to him that the formula was at least partially responsible for Norman's violent behavior. Still, he took the modified formula anyway. (Modified to increase his strength beyond that of his father's.) He didnt think of the dangers, he was focused on how he had felt small and weak for years, never getting approval from his father. He exposed himself to the formula in an attempt to become the man that he wanted to be. (Spectacular Spider-Man #188)
Psychopathology: Bipolar Disorder
Norman Osborn has been diagnosed as "massively bipolar" by Dr. Karla Sofen, aka, "Moonstone." (Thunderbolts #113) While Dr. Sofen has psychological issues of her own, she has examined Norman more closely than I have. This is relevant to Harry, as it has been shown that children of bipolar parents are at greatly heightened risk of developing the disease themselves. It was found that children with one bipolar parent are fourteen times as likely to have the disease themselves, compared to a child with two healthy parents. Children of bipolar parents are twice as likely to have a mood or anxiety disorder.
Of course, it can be hard to tell where Harry's manic depression ends and where the effects of the Goblin formula begin. What is clear is that Harry was having visual and auditory hallucinations shortly before he exposed himself to the formula. While on a family day with Liz and Norman Jr., Harry sees his father, disapproving of the fun and frivolity. The apparition asks him "Why do you indulge him like this, Harry? Zoos and merry-go-rounds. Hmph. It's a hard world out there. The sooner he learns that, the better." After Harry comes out of the hallucination, he snaps at Normie, asking "What the devil do you want?!" (Spectacular Spider-Man #179) He just as quickly snaps out of that mood and gets some cotton candy for his son.
After taking the Goblin formula, Harry's moods become even more violent. As he expected, he does become less scared and uncertain of himself. While he became the Green Goblin before taking the formula, he couldn't bring himself to kill Peter, but after the chemical bath he took, he was entirely focused on his friend's death. He also became more more aggressive towards his wife. A nervous Liz tried to tell Harry that he should get to bed and he grabbed her by the throat, screaming "Will you stop talking to me like that! Like I'm weak! Like I need coddling! I'm an Osborn, Liz! An Osborn! And the Osborns are strong! Strong enough to rule this family! To rule this city!" (Spectacular Spider-Man #200) Liz later divorced Harry when she learned he had been alive for years without telling her. (Amazing Spider-Man #582)
A Compassionate Psychopath
Norman and Harry share similar psychological profiles: both are bipolar and obsessed with killing Spider-Man. Both have experimented with dangerous chemical substances. However, Harry does show signs of compassion towards others, a trait that his father totally lacks. Harry went back to save Mary Jane and Normie when he realized that they were in the building set to explode, risking letting his enemy escape. He even respected Mary Jane's wishes that he go back and save Peter. Prior to all of this, Harry made it clear to her that while he hated her husband, she had nothing to fear from him. (Spectacular Spider-Man #199)
Harry Osborn has his work cut out for him. He needs help in dealing with his anger issues with his father, his hatred of Spider-Man, his drug use, any side effects of the Green Goblin formula and his bipolar disorder. His compassion will be the key to all of this. It has made him try to improve relations with his ex-wife, Liz. (He found a cure for her step-brother's condition.) If this compassion can be nurtured, he may well forgive the people around him and move one with his life. This will be difficult, as Norman still sees Harry as a possession and uses him as such.