Game of Thrones has apparently made a habit of killing the beloved Stark direwolves. Much like their Stark owners, the wolves have suffered at the mercy of Lannisters and Freys, have lost their home and have died heartbreaking deaths.
In the books, each direwolf is said to share some personality traits with its owner. More than that, some believe their faiths are entwined and that each direwolf is supposed to foreshadow the destiny of its Stark master. Calm down now...I'm not suggesting we're about to lose Bran and Rickon anytime soon, just that direwolves and Starks share a much deeper connection in the books than the TV show has let on.
The first direwolf to have an untimely death in the show, Lady was said to be "the prettiest, the most gentle and trusting" of the wolves, much like her owner Sansa. Back in Season 1, Lady had to pay the ultimate price because Arya's wolf attacked Prince Joffrey. On Cersei's whim, Ned Stark took it upon himself to put Lady down - since she was "of the North" and deserved "better than a butcher". In the books, Ned goes as far as sending the wolf's dead body to be buried at Winterfell, where it belonged.
Much may be inferred from Lady in regards to Sansa. She too dreamed of being a Lady herself, in the most romantic way - she was Joffrey's betrothed at the time. It was only after Sansa let go of her childhood dreams that she was able to begin coming into her own. She's now Lady Stark - for all intents and purposes - but she's no longer gentle and trusting, if her conversation with Littlefinger in episode "The Door" is any indication.
Like Sansa's, Arya's wolf represents what expectations she had for herself. Arya was never lady-like, and her 'dancing lessons' were proof of this. She wished to be a knight - a warrior even - so she named her wolf Nymeria, after the warrior Princess who led her people over the Narrow Sea and settled in Dorne. Nymeria bit Prince Joffrey, in Arya's defense, and 'a girl' sent her wolf away into the wild so that it may survive. We haven't heard from Nymeria since then on the show but, from the books, we know it formed a wolfpack that runs free - and eventually rescues a post-Red Wedding Caitlin Stark - in Westeros.
Had Arya been living a Lannister-free life in King's Landing - or even Winterfell - she would never have turned into the warrior she so desired to be. Similarly to Nymeria, Arya has left the world she once knew behind her to forge a new self. She's become every bit as wild - by Westerosi standards - as Nymeria running free in the forests. In Braavos, Arya has found the warrior within and has been working hard to shape it into the killing machine she wishes to be. And, who knows, one day she might even return to Westeros as a warrior Queen herself across the Narrow Sea.
Robb's Grey Wind
Robb Stark named his direwolf Grey Wind "because he ran so fast". In truth, Robb and Grey Wind were so in sync with each other that the Freys had them separated at the Red Wedding - to make sure things went their way. In Season 2, Tywin Lannister receives reports that Robb's wolf had killed many a man in battle, fighting alongside its master.
One other point that can be made is that Wind refers to the words spoken - or oaths taken - and that Robb did break his oath to marry one of the Freys daughters. By doing so, Robb condemned both his direwolf and himself to a Frey freak show, having Grey Wind's head put on his own beheaded body.
Being the youngest of the Stark children at the beginning of 'A Game Of Thrones', Rickon never received the proper grooming and education his siblings did. He was never taught how to be a Lord or even had the time to learn any fighting skills, for that matter. Instead, he was torn away from his home, had to survive on the road and, later, was separated from the only family he had left in Bran. Rickon, who was supposed to have grown to be a Stark Bannerman for his brothers, was brought up by a Wildling as a true shaggydog.
As for his direwolf, Shaggydog never had much play in the story. It may be said that Shaggydog refers to the term shaggy dog story, one that seems to build up to something great, but never fully reaches its potential. Such stories have a tendency to end in a most anti-climatic way - like, say, a wolf losing its head and being presented to Ramsey as a trophy.
Bran was the last to name his direwolf puppy, doing so only after he woke up from the comatose state he was put in in Season 1. The name Summer was a means to counterpart the dream he had, in which he experienced visions of a long winter, with ice all around him. Bran is also often referred to as "the sweet summer child", another innuendo to his Summer direwolf.
In the latest episode of Game of Thrones, we see Summer sacrifice itself to save Bran, Meera and Hodor - who later perished anyway. The wolf was killed by the Wights - who, alongside the White Walkers symbolize the Winter that has been predicted. Summer's demise did more than dwindle the number of direwolves in the show, it signifies once and for all that Winter has come and that the terrors of the night are a real threat.
Being the bastard son of Ned Stark - as far as the show goes - Jon Snow didn't initially have a direwolf of his own. The albino wolf puppy, that has grown into a ferocious and loyal beast, was a proper fit for a bastard. Ghost was found away from his mother and the litter, and was clearly distinct from the other wolves.
Season 5 ended with Jon being stabbed multiple times by his Night Watch brothers, left out for dead. When Season 6 returned, we found out he was indeed dead, and there are those who believe that when you die, you become a ghost. Many fans were hoping for Jon to survive by warging into Ghost, which - if he did - was never shown to us. Book fans will know that the link Ghost and Jon share is bigger in the pages than on TV, but TV fans will have gathered that Ghost and Jon are one when the wolf calmly lifted his head to acknowledge his master - just as Jon Snow came back to life.
BONUS Ned Stark and the direwolf mother
This was such an in-your-face Easter Egg back in Season 1 that, even if you weren't an avid book reader, I'm sure you grasped the Baratheon/Stark inference. When Ned and his children are returning home and eventually find the dead direwolf and its litter, they discover that the wolf had died fighting a stag - possibly protecting the puppies. Later on, Ned Stark dies at the hands of Joffrey Baratheon - Sansa Stark at his side, and the last thing he does is look for his daughter Arya amidst the crowd. Like Ned himself says upon finding the direwolf and the stag, "such a waste".