The History of "Game Of Thrones" House Stark dates way back recorded history in the world of Westeros. It's known to be as old as 12,000 years ago when the Starks were first introduced in the show. The ambiguous "winter is coming" may mean more than just what viewers think and believe it is. Much tragedies, wars, and important happenings took place before the present ongoing feud for the Iron Throne.

"I have the Blood of the First Men", proudly quoted by the "Starks" and others in "The North" is a meaningful reference to their majestic lineage.

There were actually two "First Men" groups that existed before. "The First Men", who are stocky, and robust human beings are believed to be the ones that came from the far lands who started the civilization in "The North". But before they found safe settlements, "The Children of the Forest" were already there. They are mystical non-human creatures who takes care of nature and the lands. These two engaged in war 2000 years and eventually agreed to peace.

No more conflict arose for a time, until "The Others" came in to view. According to George R.R. Martin's book "A song of ice and fire", they are what legends in Westeros cite as "White Walkers". They originated from the farthest Northern lands "Always Winter". The teamed-up "First Men" took care of "The Others" and sent them back in the Northern end.

Again peace and order is in place. Then 6000 years after "The Andals", coming from the East, invaded and pushed the "First Men" to the North. "The Andals" then settled in the South of Westeros and thus continued the present civilization except for the "Northeners". "The Andals" are presently known to be the people of "King's Landing" and most of the Southern areas.
Going back to the North, legend of the Northern ancient times Bran "The Builder" Stark, built a barricade to forever shut out "The Others" from the world. This barricade is now known as "The Wall". Bran the Builder also built "Winterfell", "Storm's End", and the House Stark Sigil. He was even credited, the "First King in the North". Ed Stark's family is originally traced to this great man.

Rickard Stark, Eddard Stark's father, planned on making an alliance with two Southern houses. These are the houses Tully, and, Baratheon. Rickard hoped to do this by arranging his oldest son Brandon Stark, Ned's older brother, to marry Catelyn Tully, and Lyanna Stark (sounds familiar?) to Robert Baratheon.

How did Ned end up with Catelyn in the story? Here's to a surprising turn of events.
Brandon, compared to Ned, is the total "wolf" blood of the Starks. He has stronger personality, and greater battle skills. During the "War of the Usurper" or known as King Robert's Rebellion, Brandon was to marry Catelyn Tully in Riverrun. But he heard a rumor that his sister Lyanna was abducted by Rhaegar Targaryen. Brandon instead went to King's Landing and banged on the castle doors looking to fight Rhaegar.

Unfortunately, Rhaegar and Lyanna weren't there, and Mad King Aerys Targaryen met the raging Brandon. After that, the Mad King captured Brandon and called for his father to answer for the rebellious outburst. The Mad King, true to his name and sigil, had Rickard burned to death, and Brandon strangled until both met their dishonorable end.

Ned Stark eventually tied the knot with Catelyn and started the present House Stark family.
This may explain and hint viewers how misfortune naturally runs in House Stark. But this doesn't mean they'll forever succumb to such a painful fate.

Westeros must remember that House Stark started it all, and they're not simply to be forgotten in the whole picture of things.
Indicative in Tyrion Lannister's words, "The Northerners will never forget", Westeros should expect the Starks will exact their due revenge in the future.