There are loads of characters in Game of Thrones that are offscreened without a single hint regarding their future (Daario, Quaithe, Jaqen H'ghar, to name a few), but for most of them, the only exit from the show is through death. Unsurprising, perhaps, but this still doesn't mean that their time on the show was well-spent.
Although there are several characters who fully reached their potential before being ejected, there are an equal number who failed to leave the slightest mark on the story. The list below alternates between ten of them.
Good Exit: Viserys Targaryen
Viserys' bravado is grating at best, with all his tall tales of being the Dragon King and heir to the Seven Kingdoms. Unfortunately for him, he does not realize what he's walking into when he demands that the Dothraki treat him like royalty.
Drogo decides to grant him his ultimate desire, and holds a mock coronation with a pail of molten gold, which simmers its way across Viserys' skull. Daenerys adds insult to injury by then claiming that her brother had not a single drop of dragon in him, implying that she would soon come into her destiny.
Terrible Exit: Cersei Lannister
Cersei, Queen of the Seven Kingdoms, the most powerful human being in Westeros (excluding Dany, obviously) meets her doom in a rather unpleasant manner.
Both she and her brother/lover are squashed by the falling Keep, held together in a final embrace. It's clear that the showrunners finished their story in a hurry, because that is quite a pathetic ending for such a magnificent character. No glimmering green wildfire, no last minute zombie army, just a pile of shattered masonry and two corpses.
Good Exit: Ramsay Bolton
The saga of Ramsay Bolton is packed with violence, daddy issues, and a complete lack of disregard for the nerve endings of his flayed victims. By the conclusion of the Battle of the Bastards, the only thing left for him is to die, but not quickly, and certainly not without some scintillating agony first.
Sansa, in all her righteous fury, lets loose the Bolton dogs against their master; they don't take him apart instantly, being unsure of what task is expected of them, but this uncertainty vanishes when they realize that what sits before them is nothing more than a heavy snack.
Terrible Exit: Melisandre
Melisandre might be hundreds of years old, but the only thing keeping her body in place is the aura of the Lord of Light. She makes several major decisions throughout the narrative: burning innocent victims at the stake, conjuring a smoke-demon to murder Renly Baratheon, to ferrying Jon Snow back into the living world.
It is Melisandre who gives Arya the courage to attack the Night King, by reminding her about the correct answer to be given to the God of Death ("Not today"). And yet, her departure is lukewarm; she basically commits suicide by means of instant aging because seemingly, she has no reason to live anymore?
Good Exit: Barristan Selmy
The honorable Barristan Selmy makes a great friend to Daenerys, regaling her with tales of warmth and comion about her oldest brother, Rhaegar. He knows when his time is up, though, given that he helps Grey Worm escape from the Sons of the Harpy, only to fight them all himself.
He successfully kills several attackers, but receives way too many battle-wounds for an old man like him to recover from. Interestingly, Barristan is not dead in the novels, and is actually seen in one of the chapters pre-released for the sixth book, The Winds of Winter.
Terrible Exit: Rickon Stark
Rickon is hardly present for most of the series, having been secreted away by Osha upon Bran's instructions. Of course there is betrayal, as Lord Umber allies with Ramsay Bolton and transfers custody of the youngest Stark to the new "Lord of Winterfell."
Ramsay employs a rather smart tactic, baiting Jon with the appearance of his brother, and tells Rickon to run away if he wants to live. He doesn't live. More importantly, is it really that complicated to run in a zig-zag fashion? He'd have died anyway, but at least he wouldn't have looked so ridiculous doing it.
Good Exit: Mance Rayder
The King-Beyond-the-Wall is no coward, willingly accepting his fiery fate if it means never having to "bend the knee" to Stannis Baratheon. Jon Snow begs him to reconsider, but Mance Rayder stays true to his word all the way to the stake.
At the point of burning, however, he begins to exhibit the first signs of fear (which is completely expected and does not diminish his bravery in any way), so Jon speeds up the job by shooting an arrow in his chest. Mance's farewell is excruciating to watch, but his death has a restructuring effect on Wildling loyalty.
Terrible Exit: The Sand Snakes
Oberyn Martell's children are no less spectacular than he is; the problem, though, is that they are also as reckless. Nymeria, Tyene, and Obara, the Sand Snakes, seem almost excited at the prospect of obtaining revenge for their dad's death, but they aren't quite sensible at going about it.
In the end, after a series of easily avoidable mishaps, these three women meet their grisly ends: Nymeria and Obara are killed by Euron Greyjoy and his men, while Tyene (along with her mother, Ellaria) is given to Cersei to receive a lingering death as a "tribute" to Myrcella.
Good Exit: Lysa Arryn
Lysa's psychotic episodes keep increasing through the first few seasons, her mind fragmenting upon with Littlefinger's creepy little manipulations. When she sees her "love" making out with her niece, she calls Sansa to the Moon Door (who is subsequently saved by the timely arrival of Baelish.)
At this point, he has obtained everything he needs from Lysa, so he decides to tell her that he was still in love with Catelyn, a last piece of agony before she is thrown out of the Moon Door. A very satisfactory conclusion to the life of a bizarrely evil woman.
Terrible Exit: Shireen Baratheon
The most painful death scene in Game of Thrones is that of Shireen Baratheon, sacrificed by Stannis (and Melisandre), so that he may obtain age for his army through the heavy snow.
The murder of his beloved child is not without consequence, as nearly half his men abandon him after watching the macabre spectacle, which is a direct cause of his inevitable loss against the Bolton army, and therefore, his death. All the potential that had been in Shireen was snuffed out by her father, and for what?