It is not uncommon for characters to have issues with their parents. That is an understatement in Lost where many of the main characters had terrible or problematic fathers. The season 1 episode "All The Best Cowboys Have Daddy Issues" is a Jack-centric episode, but that title could have also worked for many of the characters struggling with their own daddy issues.
There were plenty of bad fathers in Lost, but there were some rare gems, along with fathers who learned to be better as the series progressed. These are the main fathers in Lost ranked from worst to best.
Anthony Cooper
When a father cons his son out of a kidney and later on pushes him out of a window, that individual is unlikely to be the father of the year. Anthony Cooper only entered John Locke's life when he needed a kidney transplant. Cooper pretended to care about and bond with John, just so he could steal his son's kidney.
Cooper took advantage of John again when he needed money, which led to the end of John's relationship with Helen. When John tried to protect a family from being conned by his father, Cooper pushed John out of a window and paralyzed him. When Cooper appeared on the Island he showed no remorse for his actions and had the audacity to mock John. All of this cements Anthony Cooper as Lost's worst father.
Roger Linus
Roger's wife died soon after giving birth to Ben. Roger spent the rest of his life blaming Ben for her death. He resented Ben and blamed his son for everything that went wrong in his life.
In addition to this emotional and psychological abuse, Roger sometimes was physically abusive with Ben as well, such as when he slammed his son against the bars after he brought food to an imprisoned Sayid.
Woo-Jung Paik
Sun's father was a powerful, corrupt, and ruthless businessman. He would send "messages" to those who threatened or disrupted his business by having those individuals seriously hurt or even killed. He was a terrible person and the only thing that made him better than the likes of Anthony Cooper and Roger Linus was that he didn't abuse his child.
He nearly destroyed Sun and Jin's marriage as he forced Jin to work for him and for Jin to send "messages." This was the root of the distance, neglect, and emotional abuse that festered in Sun and Jin's marriage for far too long.
Charles Widmore
Charles Widmore sacrificed relationships with his children for what he believed was the greater good. There was tension between him and his daughter Penny and she wanted nothing to do with him. In fact, he and Penny never shared a scene together in the entire show. On many occasions, he tried to destroy her relationship with Desmond.
Widmore was also Daniel Faraday's biological father, but they never had any actual relationship. He funded Daniel's research and ensured that Daniel would go to the Island where he would ultimately have to die. Widmore did these things for the sake of the Island, for Jacob, and to preserve the timeline, but it required him to be a distant and lackluster father to his children.
Christian Shephard
Even when Jack was a kid, Christian put enormous pressure on his son, telling him that "When you fail . . . you just don't have what it takes." He constantly made Jack feel like he wasn't good enough and never would be. Christian performed surgery on a patient when he was under the influence and the patient died. He tried to get Jack to do the wrong thing and help him sweep this incident under the rug. When Jack refused and told the truth, Christian resented his son and made Jack feel guilty for doing the right thing.
What Jack didn't know--but later learned from Sawyer--was that Christian was proud of his son for doing the right thing and that he believed Jack to be a better man than him. Jack reunited with Christian in the flash-sideways, where Christian explained what was happening and he was able to reconcile with his son.
Ben Linus
Ben played an unforgivable role in Alex's death, which haunted him for the rest of eternity. He also stole Alex as a baby from her mother Danielle Rousseau. Yet, he did refuse to kill Alex when she was a baby even though it meant defying the Others' leader Charles Widmore. In order to save her and give her a good life, he committed to raising her as his own.
In the flash-sideways, Ben sacrificed his power and dedicated himself to helping Alex and being a positive role model and father figure for her. He even chose to stay outside of the church and not move on yet so he could spend more time with Alex and be the father he should have been.
David Reyes
When Hurley was younger, he worked on fixing up a Camaro with his father, who taught Hurley the importance of having hope and faith. Hurley's father abandoned the family for 17 years. When his father returned, it took a long time for Hurley to trust him again but when he eventually did, he and his dad became the best of friends.
David finished fixing up the Camaro after the disappearance of Oceanic 815. After Hurley returned with the Oceanic 6, he didn't always understand what Hurley was saying or doing, yet always he helped and supported Hurley in any way that he could.
Sam Austen
Sam Austen wasn't Kate's biological father, but he was the father figure who actually cared about her and raised her well. They shared many experiences together that helped them form a close bond and he loved Kate, regardless of the fact that they weren't related by blood.
He taught her how to track when they went hunting together, a skill that later proved invaluable when Kate was on the Island. After Kate killed her real biological father, he shared how he always loved her and gave her an hour's head start before calling the authorities.
Michael Dawson
Michael cared deeply about his son Walt. Despite the difficult situations he was put in after Susan took Walt away and when the Others kidnapped Walt, Michael tried to do everything in his power to be a good father to Walt.
He made tremendous sacrifices to protect Walt and to keep him safe. On the Island, he worked tirelessly to win his son's trust and respect. Michael's fierce love and commitment sometimes blinded him and led to poor decisions, but he tried to be the best father he could be in impossible situations.
Mr. Kwon
Mr. Kwon raised Jin all on his own. He taught Jin to be a skilled fisherman who could provide for himself and others.
Despite the challenges of being a poor fisherman and single father, Mr. Kwon always had an optimistic, cheerful attitude that never wavered. He helped Jin realize what was important and how to save his marriage with Sun. These factors solidify Mr. Kwon as Lost's best father.