The most famous is definitely Robert's Rebellion. It was a long and bloody war that changed the entire power structure of Westeros. Robert's personal vendetta against Rhaegar Targaryen was at the heart of it. He was a charismatic leader who managed to gather a large coalition of houses to fight with him.
One war story is about Robert's Rebellion. He led his forces against the Targaryen dynasty. His main motivation was the supposed abduction and rape of Lyanna Stark by Rhaegar Targaryen. Robert was a fierce warrior, and with the help of his allies like Ned Stark, he was able to overthrow the Targaryens. He fought in many battles during this rebellion, and his victory led to him becoming the king.
Perhaps their relationship begins with curiosity. Daenerys has heard of the powerful Robert in Westeros, and Robert is intrigued by this Targaryen with a claim to the Iron Throne. As they communicate more, they find common ground in their desire for a just Westeros. They might start to fall in love slowly as they share their dreams and fears, and work towards building a better future for the Seven Kingdoms.
One of the most memorable events was his victory at the Trident. His battle against Rhaegar Targaryen there was a turning point. He killed Rhaegar with his warhammer, which was a huge moment that led to the downfall of the Targaryen dynasty.
Good fanfiction about Robert Baratheon also needs to capture the essence of the world he lives in. It should include the political intrigue, the power struggles, and the cultural aspects of Westeros. If it can tie in his actions as king with the greater political landscape, like how his decisions affected the different houses, it makes for a great read. Also, delving into his vices, like his drinking problem, and how it impacts his rule and those around him is a plus.
One idea could be a story where Robert Baratheon discovers Jon Snow's true parentage earlier. This could lead to a complex relationship where he sees Jon as a potential heir or a powerful ally. He might take Jon under his wing, train him in the ways of leadership and warfare, much like he did with Ned Stark's other children.
Power is a common theme. Fanfictions often explore how Robert wields his power as king, whether he uses it wisely or misuses it. Another theme is love and lust, like his relationship with Cersei and how that affected his rule.
One aspect to consider in this fanfiction could be the clash of cultures between the Baratheon and Stark families. Since Robert is a Baratheon and the OC is a Stark, their relationship might be shaped by the different values and traditions each family holds. For example, the Starks are known for their loyalty and honor, while the Baratheons can be more power - hungry. This could create interesting dynamics in the story, such as how they handle political situations together or how they resolve conflicts that arise from their family differences.