The amount of good in the world that the Winchester's do in Supernatural is incredible. From saving families to each other to the world, they have their issues but are undoubtedly heroes. Even as individuals, they do so much good. Dean is as troubled as they come, but his selflessness, care, and skill lead him to perform a slew of heroics over fifteen seasons of the show.
Alongside these heroics, though, Dean can find himself doing wrong, making mistakes, and being more villainous than heroic, whether this is because he is not in control or because he wrongly believed he was doing good, something Sam and Cas were also guilty of.
Hero - Killing Eve
Eve is a villain who disappointed many. Despite her status as the Mother of All, she did not make much of an impact and died off pretty quickly to never return to the show. Nevertheless, Dean killing her was fairly heroic and was a risky move by the Winchester.
To kill the mysterious being, Dean ingested Phoenix ash with a shot of whiskey and goaded Eve into biting him, to which she obliged trying to turn them into monsters, which then killed her as she was poisoned by the Phoenix ash in his blood. A bold move even by Dean's standard.
Villain - The Plan To Kill Amara
Dean and Amara/the Darkness have this strange, cosmic bond that means they cannot truly hurt each other. However, that does not mean Dean cannot lie to her and send her to her death which is exactly what he does.
He lies to Amara about having a way to trap God and asks for her help which she eventually gives, trapping Chuck waiting for the Winchesters. When she finds out Dean lied and had planned to have Jack kill both her and God, she is heartbroken, and God absorbs her.
Hero - Bringing Cas Back From Naomi
Castiel is a character who is always getting in trouble and trying so desperately to do good while actually doing the opposite, sometimes being manipulated by others into doing stuff against his good-hearted nature, others like Naomi.
After a good while of Naomi basically controlling Castiel, the time came for him to kill Dean. Dean being Dean, he does not give up on Castiel or the good within him and manages to bring the real Cas back through pretty much sheer heart and will, with Cas finally realizing what was truly going on.
Villain - Constant Lies To Sam
The Winchesters have a serious problem with lying to one another. It is pretty much a constant in the show that one of the two hides something or lies about something to the other.
Dean tells Sam a lot of lies that sometimes are pretty inoffensive and unnecessary but do not cause much damage, but some do end up having consequences, like lying about Gadreel, which gets Kevin killed. There is also stuff like him selling his soul (which did not last long) and hiding the effects of the Mark of Cain.
Hero - Erasing Lisa & Ben's Memories
Dean's year of apple-pie life with Lisa and Ben was pretty much the closest he came to a family of his own and a normal life away from hunting but was never going to last.
When Sam returned, that life began to end. While they tried to make it work with Dean hunting, it soon became clear that could not happen. To protect them, Dean made the decision to have their memories of him erased, a heartbreaking choice that took so much strength from Dean.
Villain - Killing Amy
The Amy Pond of Supernatural did not so much have an appetite for fish fingers and custards like another franchise's character, more so a natural appetite for brains being a Kitsune.
Amy was an old friend of Sam's and did not kill humans. Instead, she fed on dead brains and sustained herself for years until her son needed more sustenance, and she killed people who she deemed deserving to let her son survive, and when she told the truth to Sam, he let her go. But, Dean caught up with her and her son, and killed her for her actions, warning her son if he killed, then Dean would kill him too. It was definitely a dark and unpopular moment from Dean.
Hero - Killing Azazel
The main goal of Sam, Dean, and John over the first and second seasons of Supernatural was to hunt and kill the demon who killed Mary. That was "yellow-eyes," a.k.a Azazel, a Prince of Hell.
It took a lot of hunting, and the journey saw plenty of ups and downs, including Sam, Dean, and John dying in some capacity, two demon deals, and Dean's life being cut to one year after a demon deal, but they did it. In the season 2 finale, Dean shot the Colt and killed Azazel once and for all.
Villain - Killing Cyrus
The Styne family was a short-lived but impactful family of minor villains that caused a lot of trouble for the Winchester brothers and killed Charlie. But Cyrus Frankenstein was different; he hated his family and did not want to join them.
Nevertheless, he was too young to set out on his own just yet, and so he got dragged about into doing things by his family, including going to the Bunker. There, Dean arrived after killing his whole family and killed the two other Stynes Cyrus was there with. Despite pleading for his life and claiming he was different and hated his family, Dean shot Cyrus in the head in cold blood. Of course, this was down to the Mark of Cain, but that does not make it any less villainous.
Hero - Not Giving Up On Sam
Despite everything that goes down with the brothers, including all the lies and resentment that pops up, they are always there for one another. They always have each other's backs, and Dean sees it as his responsibility in life to care for little Sammy.
The best example of Dean's care for Sam comes in "Swan Song," when he refuses to believe his brother is gone and refuses to give up on him, talking to Sam despite Lucifer beating him to a bloody pulp. Dean was a catalyst for Sam taking over his body again. There are then more divisive acts like selling his soul for Sam, stopping him during the trials, and making sure Sam goes on in life and is happy without him.
Villain - Treatment Of Jack
Jack Kline became the fourth member of Team Free Will very late in Supernatural's run. His relationship with Cas and Sam was fairly consistently full of love, but his relationship with Dean was incredibly complicated.
Dean literally hated Jack at times, and the fandom vocally disliked his treatment of Jack. He obviously comes around to Jack and treats him well, but Dean was fairly abusive of Jack at times, threatening to kill him and not supporting him emotionally. Between all that and stuff like the Jack in the box incident, Dean's treatment of Jack was far from heroic. He did not see Jack; he saw Lucifer.