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As House of the Dragon builds to a central conflict between Daemon, Aegon, and Rhaenyra, many fans are forced to think back to a conflict between other Targaryens in Game of Thrones. After all, it's the type of conflict that the show is almost certainly getting ready to showcase.
While Daenerys Targaryen and Jon Snow were certainly enemies by the end of the first show, they also both picked up numerous other foes along the way, which the three conflicting pieces in House of the Dragon will surely do as well. Jon Snow, more than anyone else in the show, made some major enemies.
Catelyn Stark
From the moment Jon Snow arrived in Winterfell as an infant, Catelyn Stark despised him. He was a symbol of Ned Stark's supposed infidelity, and Catelyn didn't know how to express that without taking it out on a boy who had done absolutely nothing wrong.
If not for Catelyn bullying Jon, it's likely he might have avoided the Night's Watch entirely. Given that he would have been forced to stay in Winterfell with a woman who wished him dead and refused to let him say a proper goodbye to his brother, Catelyn's behavior was supremely cruel and utterly unnecessary.
Cersei Lannister
Once a queen, then a mother to kings, then finally a queen again, Cersei Lannister proved to be a major threat to the North, the Night's Watch, and even to the seven kingdoms as a whole. Yet, despite everything, Cersei was a direct enemy to Jon Snow as well.
When Jon Snow revealed the existence of the White Walkers, he was promised support that would never come. It led him to plan around the hope that they would have the backing of King's Landing. Instead, he was forced to cope without additional help, despite trying to save the world. It could have meant the end of Westeros, and it's why Cersei was such an evil villain.
Mance Rayder
Though they spent a long while walking together, and Jon even spared Mance's agony by shooting him before he could be burned to death, they were still enemies. Mance was an honorable character, but his goals were entirely against the interest of Jon and the Night's Watch, and it's why the two spent so long at odds.
Mance wanted to bring down the Wall or tear open the gates, so he could bring the Free Folk south, but Jon needed to keep to his vows. It's why Jon fought Mance, and it's why Mance was perfectly happy to see Jon either die or fail. The two could have sought peace, given Jon's later support of the Free Folk, but they never managed to recover.
Ramsay Bolton
One of the most brutal characters in Game of Thrones, Ramsay became a major enemy to Jon Snow. After capturing Winterfell, Ramsay sent Jon a threatening message demanding Sansa back and threatening to kill the newly-captive Rickon Stark.
Having done the worst thing Ramsay could do by threatening the Starks, he became Jon's instant enemy. Ramsay was also arrogant to realize that it would lead to a war that Ramsay could not truly win, thanks to the Stark support in the Vale. Thankfully, Jon was able to take Ramsay down, but it only came after Rickon's death.
Orell
Jon spent most of Game of Thrones bearing claw-shaped scars along his face, and it only came because the skinchanger Orell launched after him in an eagle's body. The wildling had always distrusted Jon, thanks to the fact that Jon arrived in the wildling camp as a man of the Night's Watch.
While Orell was right about Jon, that still didn't stop him from losing his life when Jon finally decided to betray them all. Still, Orell haunted Jon from beyond the grave in the form of his eagle. Though Jon stopped Orell's bird, it still marked him for life and could easily have killed him, had things gone even slightly differently.
Janos Slynt
One of the least competent Game of Thrones villains, Janos Slynt was utterly determined to undermine the newly-elected Lord Commander Snow. So, when Jon commanded that he take leadership of a ruined castle, Janos refused the command and elected to stay in Castle Black.
In the end, the only resolution was that Jon had to take Janos' head in response to the noncompliance. Had he not, he might have lost the chance to earn the respect of the Night's Watch, and Jon would have been a puppet leader for Janos and Alliser. While Janos was also pathetic for it to actually work, he certainly made an enemy of Jon.
Alliser Thorne
Jon's enemy from the start of his time in the Night's Watch, Ser Alliser was never a fan of Ned's illegitimate son he named "Lord Snow." Thanks to his grudge against the Starks, he despised Jon and was even pleased to see him stuck on the stewards, instead of given a position on the rangers.
Given that Alliser was more than happy to bully Jon and Sam, he absolutely was Jon's foe. The fact that he was later willing to participate in a mutiny against his own Lord Commander only further worsened their relationship, which is why it made so much sense that Jon was willing to hang him for it.
Olly
A little boy that Jon took in as his own steward after the Free Folk attacked his village, Olly looked like a true ally for Jon. Since the boy was being groomed for command, much like Jon was, it seemed he would really thrive within the Night's Watch, and Olly even put himself at risk by killing Ygritte for him. Yet, Olly betrayed Jon's trust after Jon welcomed the Free Folk south.
After participating in the mutiny, Olly proved that he was a genuine enemy to Jon. Despite Jon putting his trust in the boy, he was completely betrayed for his vulnerability. It was clear that it hurt Jon to hang the boy, especially given how close they were prior to the heel-turn.
Daenerys Targaryen
Once a woman that Jon truly did love, Daenerys was a friend and ally. Jon was even willing to bend the knee to her, after she proved willing to rescue potential enemies in order to save the Seven Kingdoms from the threat of the White Walker invasion.
Yet, after Daenerys burned King's Landing, Jon showed that they were enemies by outright murdering Daenerys. Jon's place as a secret Targaryen contributed to Daenerys' downfall, as it drove her to the brink. Had they been able to resolve the issue, they may have lived a long life together. Instead, thousands died over Jon's relationship with Daenerys, and Jon paid the price.
The Night King
Jon Snow's worst enemy is undoubtedly the ruler of the White Walkers, the Night King. Given that Jon spent all eight seasons of the show preparing for the fight against the Walkers, the leader of the entire dead army was certainly the strongest of Jon's enemies.
From the moment Jon faced off against him at Hardhome, it was clear that the show was building towards a bloody conflict between the two. Given how fierce the fighting was in Winterfell, they were undoubtedly serious opponents, and it's hard to point to any foe that posed a greater threat to Jon than the one who raised all of his ancestors and tried to kill his family.