Jaime Lannister's incestuous relationship with his twin sister Cersei on Game Of Thrones had devastating consequences for almost everyone in Westeros. The Kingslayer's affair with the Queen of the Seven Kingdoms results in the War of the Five Kings after Ned Stark discovers the true parentage of Joffrey, Myrcella, and Tommen.
There were certainly several other characters who would have been a better partner than Cersei. The evil queen was a toxic influence who brought out the worst in Jaime. These powerful players in the game of thrones would have been more interesting - if unlikely - matches with the Kingslayer.
Lysa Arryn
In the A Song Of Ice And Fire book series, Tywin Lannister attempts to force his son Jaime to marry Lysa Arryn. This union would have rectified the rift between House Lannister and House Arryn as well as bring the Knights of the Vale into the war with the Starks.
Lysa Arryn was one of the most powerful ladies in Westeros before her death. As the mother of Robin Arryn, the heir to the Eyrie, she commanded the Knights of the Vale and would have been a valuable ally.
Lyanna Stark
Game Of Thrones would be a very different show if Jaime Lannister had married Lyanna Stark in his youth instead of pursuing Cersei and joining the Kingsguard. Ned and Jaime would be brothers by law. Houses Lannister and Stark would have been united, preventing the War of the Five Kings long before it began.
Lyanna Stark's secret marriage to Rhaegar Targaryen was one of the central catalysts for Robert's Rebellion. If the Northern lady had wed the heir to Casterly Rock, then the Targaryens might have remained on the Iron Throne, with Rhaegar eventually overthrowing his mad father.
Elia Martell
Another marriage pact that never came to fruition from the books is the betrothal of Jaime Lannister and Elia Martell. Jaime and Cersei's mother Joanna initially intends to marry her twins to Elia and Oberyn. Tywin rejects this promised union after her death, which upset the Martells in Dorne.
If Jaime had wed Elia instead of conspiring to join his sister in King's Landing then Rhaegar Targaryen would have been free to marry Lyanna Stark. House Lannister could have been allied with House Martell instead of at war.
Sansa Stark
Jaime Lannister swore an oath to Catelyn Stark that he would protect her daughters. Tywin forces Tyrion to marry Sansa, which results in her being accused of murdering Joffrey after Tyrion's arrest. If Jaime had married Sansa instead, then it is likely he could have protected her better, upholding his vow to Catelyn.
This union was never likely considering the bitter hatred between the Lannisters and the Starks but it would have been a symbolic conclusion to the war. Sansa becomes a powerful political figure towards the end of the series and would have made a valuable ally.
Catelyn Stark
This is another unlikely union that would ultimately have brought far less bloodshed than Jaime's incestuous romance with Cersei. Jaime is taken hostage by Robb following the Battle of the Whispering Wood and remains a captive in the Northern army until his release.
Catelyn despised Jaime yet the Kingslayer admits, later on, to have had a great deal of respect for her. This alliance was another opportunity to unite House Stark and House Lannister, putting aside animosity in time to fight the Night King.
Daenerys Targaryen
Admittedly, Jaime and Daenerys have a bitter history. Jaime earned his moniker as the Kingslayer by betraying and killing Dany's father Aerys. The two fought against each other during "The Spoils of War," with Jaime charging directly at the Mother of Dragons before narrowly avoiding Drogon's fire.
An alliance between Daenerys and Jaime would have been the ideal union to heal the wounds of the past and prevent more bloodshed during the Dragon Queen's conquest. The war between Cersei and Daenerys resulted in fiery devastation. This relationship could have prevented one of the series' most controversial moments.
Margaery Tyrell
Margaery Tyrell was one of the most adept political players in the Seven Kingdoms before her fiery death in the Sept of Baelor. She was smart and had the might of the Reach behind her. A match between Jaime and Margaery would have been another, more interesting way to unite two of the most powerful families in Westeros.
Tywin understood the value of House Tyrell's loyalty and rewarded their aid by marrying Margaery to Joffrey and Tommen. Although Margaery wanted to be queen, she would still be one of the show's strongest characters with Jaime at her side.
Bronn
Bronn was initially Tyrion's friend, but he and Jaime strike up a bromance of their own in season five after journeying to Dorne to rescue Princess Myrcella. The sellsword claims to be out for himself several times but he saves Jaime from a dragon when Daenerys and the Dothraki ambush the Lannister forces following the siege of Highgarden.
Cersei hired Bronn to kill Jaime and Tyrion but the sellsword still spared their lives. He reaps the rewards of his decisions in the series finale when he officially becomes the new Lord of the Reach.
Roslin Frey
Roslin Frey was initially promised to marry Robb Stark and, had the King in the North honored their betrothal, the War of the Five Kings may have had a different outcome. Roslin instead married Edmure Tully, who was thrown into a dungeon cell on his wedding night whilst his family was slaughtered.
Tywin Lannister orchestrates the Red Wedding and becomes strong allies with House Frey. A marriage between Jaime and Roslin would have honored this alliance as well as keeping the Kingslayer away from his toxic sister.
Brienne Of Tarth
Jaime and Brienne shared significant chemistry during their scenes together, despite their characters despising each other. They travel through the Riverlands before being captured by Locke. Their journey forged a connection between the two based on mutual respect and genuine care, and Jaime's relationship with Brienne could be considered his healthiest.
The two knights give into their feelings in season eight's "The Last Of The Starks" and finally sleep together. However, the Kingslayer abandons Brienne and leaves Winterfell to return to Cersei.