Jason Todd, also known as Red Hood (and formerly Robin) is one of the most controversial characters in DC comics. He has walked on the good side and on the bad, and he has garnered his fair share of admirers as a result. His relationship with Batman, for better and for worse, has been memorable, and his resurrection is not one that would easily be forgotten. What distinguishes Jason Todd from other characters is that he was a wildly popular Robin who lost his popularity because of his trigger happy and knee-jerk reactionary character.
As the Red Hood he came into a new era, one where he could fully explore his good side and dark side without being held at arm's length by Gotham's neighborhood Batman. And it was this change that opened him up to become the very ruthless and often self-serving character as he's known to be today.
10 When He Abducted And Tortured The Joker
In Batman: Under The Hood, Jason Todd has come back from the dead and he wants vengeance. While Black Mask has control of Gotham's criminal underworld he is facing resistance from a figure called Red Hood, who destroys the top floor of Black Mask's criminal headquarters with explosives. But this move pales in comparison to the torture he inflicts on The Joker. Todd is burning with so much anger and bitterness that Batman didn't avenge his death. And because Batman didn't go after The Joker, Todd decides that The Joker has to pay for what he did.
The Joker felt the brunt of Todd's anger as Todd hit him repeatedly with a crowbar to the head. When Batman arrives, Todd tells Batman (after tossing him a gun) that he must either kill him (Todd) or save The Joker on the count of three. At the count of two and a half, Batman throws his Batarang at Todd and Joker triggers explosives in the building. Todd gets institutionalized and escapes to live on the streets and then Ra's al Ghul and his daughter, Talia takes Todd and cares for him for a year. Then Talia puts him in the Lazarus pit, resulting in a more vicious and ruthless Todd/Red Hood. When he is face-to-face with Batman again Batman beats him.
9 When He Attacked Tim Drake and the Teen Titans
In Teen Titans #29, Todd's vendetta against Batman (and his seeming lack of care or remorse for his death of sorts at the hand of The Joker) extends to all Robins (but particularly Tim Drake). Drake (Robin #3 and Red Robin), was first on Todd's list. He started to go after Drake because the thought that he (Todd) would be replaceable was too much for him to bear. So when Todd shows up at Titan Towers dressed in his Red Robin uniform, he seriously maims the Teen Titans and tears the Robin symbol off of Tim Drake's outfit while he was unconscious.
He even leaves a message saying "Jason Todd was here." His jealousy of Tim Drake is intense and it almost blinds him with rage, making him a vicious and dangerous threat to this Robin (and other characters who have taken on the mantle of Robin).
8 When He Dressed Up As Batman and Committed Violent Crimes
In Batman: Battle for the Cowl, Batman has died or disappeared and everyone is scrambling to find a new Batman. And when Dick Grayson refuses to touch the Batman Cowl, choosing to avoid the Batman mantle at all costs, someone dressed as Batman begins committing violent crimes in Batman's name and image. Todd's Batman is attacked by Damian Wayne (who wants to prove is worth to Dick Grayson) and Todd shoots him and he is seriously injured.
After all this, Tim Drake takes on the mantle of Batman and finds Todd in a strange makeshift Batcave. Drake gets attacked and seriously hurt by Todd, and then Todd waits for Nightwing to come, attacking him upon his arrival. The act of dressing as someone who you used to respect, and committing crimes while pretending to them, is taking things too far. He can't shake the bitterness of being the second fiddle.
7 When He Antagonized Speedy So She Would Partner With Him
After the events of Infinite Crisis, Todd returns back to his evil, vindictive, and manipulative ways. So, in Green Arrow #72, Todd visits Green Arrow (Oliver Queen) and Speedy (Mia Dearden) to try and convince Speedy that she could be greater as his evil c0-counterpart. Todd explains to Speedy that both himself and Mia both come from similar backgrounds (the streets, where they did tough things to make it), and he explained that they both have been overlooked and underutilized and respected as sidekicks.
He explains that if she was to join him in his lifestyle that they would do great things together. This conversation is going on as Mia is engaging in combat with Todd, and she's angry (because her past includes prostitution, drugs, and a lot of murder). When she refused to join him in his ways, Todd blows up Mia's school.
6 When He Took Excessive Delight in Violence
In The Dark Knight Returns: The Last Crusade looks at a worn-out and tired Batman and his relationship with Jason Todd (Robin at the time). Bruce is feeling his age, and he knows he will eventually have to stop this vigilante gig, and he is also aware that his Robin (Jason Todd) is not interested in taking the job after him. Todd loves violence too much (a direct opposite to Batman's character) and his bloodlust is unsettling to Batman.
Todd is also careless and wayward in his role as Robin and that unsettles Batman too. He uses extreme force in his dealings with criminals, he hurts innocent people (who were ensnared by Poison Ivy's powers) and he violently crushes someone's head in a car door. The violence is scary, graphic, and excessive, and he seems to have no impulse control when he is doing it.
5 His Total Violence In Under The Hood
In Batman: Under The Hood readers see more of Jason Todd's dark side. He is excessively ruthless in his treatment of criminals, and it's hard to reconcile in a former Robin. This story takes place after Todd resurrects from the dead. Todd, a self-serving character hell-bent on revenge is full of bloodlust and decides to go after all the criminals in Gotham. His first target was Roman Sionis (Black Mask), as part of his master plan to gain access to some of the crime boss' territory for himself.
He is The Red Hood after all, and he has to show force and cruelty to get his agenda across. As the Red Hood, he violently attacks The Joker, takes the head off of eight of Black Mask's goons, and receives the attention of Batman (to who he reveals himself).
4 When He Went on A Rampage
In Batman #410, Jason Todd finds out that his father (a petty criminal who did jail time and never returned home after time was served) was killed by Two-Face. Rather than show restraint and respect for Batman (who had given him a calling and a purpose), he gets angry at Batman for not telling him that Two-Face killed his father becomes extremely destructive until he comes face-t0-face with Two-Face.
Although he ultimately lets Two-Face get arrested, the fact that he went on a rampage was almost foreshadowing for what he would become.
3 When He Pushed A Dangerous Criminal To Kill Himself
In Batman #424, Todd (as Robin) happens upon a gruesome scene: Felipe Garzonasa is a student who assaults a woman and it later causes her to commit suicide. Todd, feeling justifiably incensed by the crime and the criminal who perpetrated it, goes after him and he finds him on the apartment balcony. Things get murky when not long after the chase, Garzonasa falls to his death.
It is highly likely that Todd pushed him out that window, and in doing so he goes against Batman's vow to not kill who he captures. Todd has a history of being trigger happy so it's not a great leap to imagine him executing his own kind of violence. As terrible and disgusting as this criminal was, it technically should have been up to the authorities to decide what would become of him.
2 When He Planted A Bomb Under The Batmobile
In Red Hood Lost Days Todd uses an advanced military arsenal to produce the fake appearance of a gunrunning ring so that Batman can intercept it. Grabbing the bate, Batman goes and stakes out the location and while he's investigating Todd plants a bomb under the Batmobile. When Batman gets back in the Batmobile, he learns that there is a bomb under his vehicle and he's at the mercy of the bomber (Todd).
The only thing that makes Todd decide not to detonate the bomb is that Batman wouldn't know who killed him. He decides, instead, to kill him head-on. Todd looked all over the world for the kind of training that not even Batman can overcome, and spent years learning from combat masters, martial artists, acrobats, assassins, flight experts, poison, gun, bomb, and medical toxin experts.
1 When He Partnered with Hush & The Riddler
In Batman: Hush, the central storyline is that there is an unknown titular villain menacing Batman and Gotham City. By the end of the Hush storyline, it is revealed that the mysterious titular villain is Edward Nygma (The Riddler), Jason Todd has come back from the dead and is working with Dr. Thomas Elliot (Hush and Bruce Wayne's childhood friend) and The Riddler.
Jason Todd also told betrayed Batman further by sharing his true identity (as Bruce Wayne) with Hush and The Riddler. This may not be the bloodiest or the most violent thing he has done, but it was the most shocking and the cruelest thing he's done (as he betrayed his former teammate in such a horrid way and did it with one of Bruce Wayne's childhood friends).