The world of A Song of Ice and Fire is ever expensive and, thanks to the tireless work of George R.R. Martin, this book series has been blessed with tremendous characters written fantastically well. Game of Thrones, being the television adaptation of the novel series, sees the vast majority of these characters make an appearance and play a significant role.
However, there are certain characters who, for some reason, did not make an appearance in the show at all. Some of these characters are ones that affect the plot of the books significantly and their exclusion from the show changes the trajectory of the plot completely. As fans know already by this point, the show and the books are different canons and while the show has already concluded, it is sad that these characters never made the cut.
5 Lady Stoneheart
Lady Stoneheart is a character that plays a significant role in the books. While technically she does appear in Game of Thrones as Catelyn Stark, her story ended at the Red Wedding when a knife was put to a throat and she died, alongside her son, the King in the North, Robb Stark.
In the books, she is resurrected with the power of R'hllor, the Red God. Beric Dondarrion gives up his life for hers with a kiss of life and thus, Lady Stoneheart is born. As her name indicates, she is a character with a very cold heart and a cruel personality. She seeks revenge for what happened to her family and is pivotal to the plot going forward, as even George himself admitted.
4 Victarion Greyjoy
Victarion Greyjoy is one of the most important characters in the books. The Greyjoy plotline was utterly ruined in the show and, as such, it is not a big surprise that Victarion never made it to the show. He is a character who, in the books, is currently on the way to Mereen. He has the horn to bind the dragons to himself with magic and he intends to propose to Daenerys as well.
Victarion has great ambition and he is certainly a man who will make a significant difference in the story moving forward. Unfortunately, he never made it to the show for some bizarre reason.
3 Young Griff
In the television show, it is made abundantly clear that Rhaegar Targaryen's children were murdered before their mother, Elia, was murdered as well. This was thought to have ended the line of the Targaryens, before Daenerys and Viserys were sent to the Free Cities. In the books, however, it is believed that Varys, the Spider, smuggled Rhaegar's son, Aegon Targaryen to the Free Cities.
Varys is a supporter of the Targaryen restoration and, currently, he is backing Young Griff, who is actually Aegon. Tyrion meets with Young Griff in the fifth book and it is revealed that this boy has a certain charm about himself. He is currently the leader of the Golden Company and plans to invade Westeros very soon. Sadly, his plotline was completely erased from the show.
2 Jon Connington
Jon Connington never existed in the show as he's linked to Aegon Targaryen. It is believed that Jon Connington was a very close aide of Rhaegar and, thus, plays a significant part in watching over Aegon. Once Aegon was safely brought to the Essos, it was none other than Jon Connington who looked over him and oversaw his growth. The man that young Griff is today is down to him.
Jon Connington also aims to get Aegon married to Daenerys to solidify his claim to the Throne even further, just as he was in securing the services of the Golden Company, a group of powerful sellswords. In the show, sadly, Jon Connington does not exist at all.
1 Arianne Martell
Arianne Martell is, quite possibly, one of the saddest exclusions from the Game of Thrones TV show. The entire Dornish plotline left a bitter taste in the mouths of the fans as it was, by far, the worst part of the show. Dorne has tremendous potential and the books' handling of it has been completely different from what the show accomplished.
One of the characters who play a significant role in the Dornish plotline is Arianne Martell, the eldest daughter of Doran Martell, the Prince of Dorne. In the books, Trystane, his son, ends up dead following an attempt to tame Daenerys' dragons. This means great things for the character Arianne as she is now the rightful heir to Dorne. Undoubtedly, she is going to play a significant role in the books going forward. In the show, however, she was never even mentioned.