Barristan was the commander of the Kingsguard. Despite his age he was still one of the best knights in the Seven Kingdoms. He was also a very likeable person with a calm and kind nature. I was really surprised to see him with Dany. That was a very interesting twist. I hope he'll get more stuff to do next season because he he is such a skilled warrior.
"as Barristan Selmy. It's hard to take him seriously as "one of the best fighters in the Seven Kingdoms", when he really just looks like an old man, but he has great moments in the show. His open defiance of King Joffrey and welcome inclusion into Dany's inner circle bring him up the list.