Although the Hardys were kings among the first men, they have been loyal allies of the Starks since a cementing marriage ages ago. Lord Hardy, it was said, had no dowry to pay for his daughter's hand to Lord Stark except his eternal loyalty. The Stark's accepted the offer in the spirit it was intended, and have repaid loyalty with loyalty ever since. Rivaly with the Draupauds over the ownership of contested lands between their estates goes back almost this far, matters which the Starks choose to stay out of so long as both Houses don't get too out of hand.
It is rumored that the ancestral Hardy castle predates the era of Bran the Builder.
It is said there has always been a Hardy at the Wall.
During Robert's Rebellion, the Hardys sided with the Starks, and hence Robert. This was quite fortunate, considering how the war concluded, but even if the Starks were to challenge the whole realm, it would be in keeping with their ancient traditions to stand with the Starks and hold their ground until shattered by much larger forces.
Recent personal history is accounted here.
The Hardys have never been great readers. Wisdom internalized, such as Maesters possess, is valued much more highly than the books they read to get there. The concrete and material are valued highly, and books are seen as ephemeral.
Even compared to other northern lords, the Hardy's 'Hold Fast' to the old gods. While the opinions of individual family members show the usual degree of variance, Septons are not held in high regard. Generally, however, they are smart enough to bite their tongues on this particular subject.
This longstanding devotion for the old gods is reflected in a number of longstanding family traditions:
When war came to the north, the Hardy's were always ready to hold the most impossible, often suicidal, positions while the Starks rallied reinforcements. Tales are still told of battles in which a small group of Hardy men held a pass, or sometimes a hill or ford, against a much larger force of Southron mercenaries, impossibly large hordes of Wildings, or men from the Dreadfort.
Similar tales circulate around the Wall about last stands of scions who bore the Hardy name, and many Hardys treat all men of the Black Watch as distant cousins.
Some say that Hardy knights will stand atop a hill and hold their ground against dragonfire itself, the quintessential force which breaks the morale of armies. Of course, the Hardy knight always dies in those stories...
All Houses must have their sources of income, whether that means Lannister gold or the trade and fishing conducted in the fork by simple men who answer to the Tullys. House Hardy controls lands rich in timber, and the roads from the mines in the nearby mountains run straight to Holdfast Castle. It was from these same mountains, it is said, that the stones for the castle were cut long ago, and there still exist active granite quarries. Trappers also sell their wares near Holdfast, and a fraction of this trade makes its way into the Hardy coffers.