UPDATE 5/13/2019: We published this list before the final season, and most all of it was made impossible by the events of S8E5, "The Bells".
There are tons of theories about how individual characters might die, but one in particular has been around for decades and refuses to go away: That Jaime will kill Cersei, ending their tragic sibling love affair in a brutal act for the good of the realm. Many people believe Jaime is the one who will finally kill the series’ worst villain, because he's the answer to an important question: Who is the valonqar?
Maggy the Frog, a woods witch with prophetic powers, makes several predictions about Cersei’s life that come true, and a few that haven’t yet. The predictions are more detailed in the books than they have been in the show, and they include a section about the valonqar (High Valyrian for "younger brother") choking Cersei to death. Cersei herself believes Tyrion is destined to kill her, but the Jaime = valonqar theory is much more popular. With the mountains of evidence supporting it, it’s easy to see why.
Maggy the Frog also made a prediction for Melara Hetherspoon, Cersei's companion on that ominous night:
Melara: Will I marry Jaime?
Maggy: Not Jaime, nor any other man, Worms will have your maidenhead. Your death is here tonight, little one. Can you smell her breath? She is very close.
Cersei’s childhood friend died almost immediately afterwards. Maggy also correctly predicted the number of children both Cersei and her king, Robert, each have, along with the deaths of Joffrey, Myrcella, and Tommen. Cersei clearly believes in the prophecies of Maggy the Frog, and with good reason.
Even if the Valonqar Prophecy is meant to refer to a "younger brother," and specifically Cersei’s younger brother, there are actually two candidates. Because while Cersei and Jaime Lannister are twins, it is specifically noted that Cersei emerged from their mother’s womb first, which makes Jaime technically the younger sibling. Although Cersei never makes the connection herself, many readers have figured out that Jaime is, in fact, the most likely candidate to fulfill the Valonqar Prophecy and end his sister’s life.
It is worth noting that Jaime is no stranger to murdering a monarch. Jaime is infamously known as the Kingslayer for killing the Mad King Aerys II Targaryen, which he did to prevent Aerys from burning the population of King’s Landing. If any would-be ruler in Westeros deserves the title of “Mad” these days, it’s definitely Cersei.
She has already committed multiple brutal acts – including torturing her enemies and destroying the Great Sept (with the Mad King's own stores of wildfire, no less) – and it might not take much more to convince Jaime she’s a danger to the realm. Many theories about Jaime being the valonqar involve Cersei deciding to burn King's Landing and all the people in it just to prevent Daenerys from taking over. In this scenario, Jaime will once again murder a monarch to save the realm.
The two versions of Jaime that appear in A Song of Ice and Fire and Game of Thrones are very different characters. While Jaime’s love affair with his twin sister is still very much ongoing in the show, the book version of Jaime doesn’t feel the same. In the books, Jaime learns from Tyrion that Cersei had been sleeping with their cousin, Lancel, along with a few other men, including “Moonboy, for all I know.”
This information drives Jaime to bitter feelings about Cersei, and his private thoughts reveal he now thinks of her as the “Queen of Whores.” While Jaime returns to King’s Landing at Cersei's request in Game of Thrones, the books see Jaime ignore her calls for help while imprisoned, which has fueled speculation he is already more than willing to kill her.