A popular King Robert Baratheon, who was married to Cersei at the start of the show. Though Cersei and Gendry never interacted, there's plenty of evidence ing the biological parent theory.
Gendry was introduced in Game of Thrones' debut season as a blacksmith that worked in King's Landing. The young man was unaware of his lineage other than the fact that his mother was dead. Gendry later learned from the Red Priestess Melisandre that he was an unacknowledged bastard son of the former deceased king. Though he referred to himself as "Gendry Rivers," which was the wrong bastard name, Gendry was legitimized as a Baratheon after his efforts in the Battle of Winterfell. As a result, Gendry became the last living member of House Baratheon and the Lord of Storm's End.
Throughout Gendry's rise in nobility, starting from a resident of Flea Bottom to the head of a noble house, Cersei was focused on propelling House Lannister to power through the Iron Throne. Following the death of Robert, Cersei's sons, Joffrey and Tommen, had stints as the king. Both boys died, as did Cersei's only daughter, Myrcella, but none of the kids were fathered by Robert. Instead, the trio was a result of Cersei's incestuous relationship with her twin brother, Jaime Lannister. As pointed out in the theory (via Reddit), Cersei revealed in season 1's "The Kingsroad" that her and Robert's first son ed away during infancy. More interesting was the fact that Cersei told Catelyn Stark that that boy had black hair, which matched Gendry's description. Further details presented in the series have made the theory even more compelling, and even Dempsie recently ed the belief in an interview (via NME).
The Evidence ing Cersei Was Gendry's Mother
Whereas Gendry didn't learn of his heritage until later in life, Robert never got the opportunity to discover his son's existence. The only aspect of his parents that Gendry ed was the fact that his mother had blonde hair. Even Dempsie figured his character's line of dialogue pointing out a hair color was a significant reveal that was never fully investigated. Not only did both characters mention their respective hair colors, but there was also a plausible explanation of why Gendry grew up an orphan. If Cersei did give birth to Robert's biological son, the theorizers believed that she willingly gave the baby up, leading Robert to believe the infant ed away. This would be Cersei's sadistic action in only raising kids that were fathered with Jaime, giving only Lannisters the chance at the Iron Throne.
It was also possible that Cersei served as the unknown donor that paid for Gendry's blacksmith apprenticeship as a way to keep him distracted from learning the truth. While Game of Thrones never confirmed that Cersei and Gendry were related, it's always possible in the book series. There was less substantial evidence ing the theory in GRR Martin's ASOIAF novels, but the books did make it a point to mention how Cersei would dress as a tavern wench to meet with her brother in secret. Gendry, coincidentally, was said to be the son of a tavern wench in Martin's work, so the groundwork for the theory still exists.