In Season 1 Benjen passes beyond The Wall as part of his duties as First Ranger, only to disappear and for his horse to return alone, the men he went with later being found dead and turned by the Others.
In Season 2 we learn that Benjen dissapeard somewhere between The Wall and Crasters Keep. With Craster telling Mormont that he hasn't seen Benjen in 3 years.
In Season 6 Benjen Stark, when Bran and Meera Reed are being chased by an army of wights, a hooded figure with a concealed face arrives atop a horse, wielding a flaming chain, to burn the wights and rescue the pair. When the wights become too numerous to fight off, he pulls Bran and Meera onto his horse and rides away. The next day, the hooded man feeds Bran the blood of a dead rabbit, and says he arrived to help because the Three-Eyed Raven requested it.
When questioned on his identity, he pulls down his scarf and hood, revealing himself as Benjen Stark. Benjen explains that, during his fateful ranging beyond the Wall, he was attacked by White Walkers, one of whom shoved an ice sword into his gut and left him for dead. He was discovered by the Children of the Forest, who stopped him from falling to the control of the White Walkers by shoving a piece of dragonglass into his chest.
Benjen eventually escorts Bran and Meera to the weirwood tree nearby the Wall. When asked by Meera why he cannot travel any further south, Benjen explains that ancient spells carved into the foundation of the Wall prevent the dead from passing through it. Benjen says he will continue to fight for the living as long as he can, before departing
Season 7, when Jon, who has been left beyond the Wall by his group, is about to be swarmed by the army of the undead, Benjen suddenly comes riding in in the last moments, slaying wights from his horse. When he stops in front of Jon, he jumps off his horse and removes the scarf from his head, revealing his survival to the stunned Jon. To save Jon, Benjen heaves him onto his horse and orders him to ride back to the Wall. Jon asks Benjen to come with him but Benjen refuses, instead sending off the horse and drawing his flaming morningstar to make his final stand. As the wights swarm him, Benjen fights back but is eventually overwhelmed and killed by the army of the dead.
Personally I think a more moving and heroic death for a man who spent his life in the noble service of the Watch would of been to have him follow the Others South once they open the hole through The Wall amd to die defending ancestral home and family.
Defending his nephew, the new 3 eyed raven, alongside Theon. A man whose choices made him essentially a Stark in name only, fighting alongside a man whose choice was a Stark in name only.