The North remembers
There is a long history to the Night's Watch, and the North remembers.
Thanks to the children, the first men of the Night's Watch banded together and were able to fight—and win—the Battle for the Dawn: the last battle that broke the endless winter and sent the Others fleeing to the icy north. Now, six thousand years later (or eight thousand as True History puts forward), the Wall made to defend the realms of men is still manned by the sworn brothers of the Night's Watch, and neither the Others nor the children have been seen in many centuries.
That [the Others] became monstrous in the tales told thereafter, according to Fomas, reflects the desire of the Night's Watch and the Starks to give themselves a more heroic identity as saviors of mankind, and not merely the beneficiaries of a struggle over dominion.
The World of Ice and Fire - Ancient History: The Long Night
The history of the Night's Watch is a long one. Tales still tell of the black knights of the Wall and their noble calling. But the Age of Heroes is long done, and the Others have not shown themselves in thousands of years, if indeed they ever existed.
The World of Ice and Fire - The Wall and Beyond: The Night’s Watch
The Starks and the North remember the history upon which the Night's Watch was born. A brotherhood sworn to protect everyone, regardless of allegiances from the forgotten terror that lies in the forgotten North.
The allegiance of the Night's Watch to the realm is noted on by Visenya, when she models the Kingsguard vows after those of the Night's Watch. However instead of the realm, the Kingsguard are sworn to the King.
She modeled their vows upon those of the Night's Watch, so that they would forfeit all things save their duty to the king.
The World of Ice and Fire - The Targaryen Kings: Aegon I
It was the North that was directly in line to get rekt by the Others, and the Nights Watch were the ones protecting them:
The northern boundary of the Stark domains was protected by the Wall and the men of the Night's Watch
The World of Ice and Fire - The North: The Kings of Winter
This point was extended in a tweet by Elio and Lindo @westerosorg:
It's also a recognition that the wall has helped protect the North from wildling invasions much more recently than when the Others were last seen. It's an honorable (sic) calling for a younger son, who otherwise has few prospects, to take the black because of this history
Tweet from @westerosorg
It is for the most part unclear why they honour it so, but just that they do.
Wildling raids may rightly be considered more of a nuisance than a menace; many wise men suggest that they might be better dealt with by allowing the lords of the North to extend their rule beyond the Wall so that they can drive the wildlings back.
Only the fact that the Northmen themselves greatly honor the Watch has kept it functioning, and a great part of the food that keeps the black brothers of Castle Black, the Shadow Tower, and Eastwatch-by-the-Sea from starving comes not from the Gift but from the yearly gifts these Northern lords deliver to the Wall in token of their support.
The World of Ice and Fire - The Wall and Beyond: The Night’s Watch
The extent to which it was deemed honourable in the days of old is remarked on by Jon, when discussing the Shieldhall. Where the old Shields of knights and nobleman who'd given up their Houses for the black would hang their shields, until their death,
The Shieldhall was one of the older parts of Castle Black, a long drafty feast hall of dark stone, its oaken rafters black with the smoke of centuries. Back when the Night's Watch had been much larger, its walls had been hung with rows of brightly colored wooden shields. Then as now, when a knight took the black, tradition decreed that he set aside his former arms and take up the plain black shield of the brotherhood. The shields thus discarded would hang in the Shieldhall.
Hundreds of knights meant hundreds of shields. Hawks and eagles, dragons and griffins, suns and stags, wolves and wyverns, manticores, ... , and a hundred other heraldic charges had adorned the Shieldhall walls, blazoned in more colors than any rainbow ever dreamed of.
But when a knight died, his shield was taken down, that it might go with him to his pyre or his tomb...
A Dance with Dragons: Jon XIII
The Southerners have long forgotten the threats of not only the Others, but of the Wildlings, they mostly consider it to be folk stories and old wives' tales. The Southron lords have only known the Northern realm to be their threat from the North (before Aegon's Landing) since the Night's Watch and the North had kept everything else at bay. This ignorance was, however, not always the case, as the description of the Shieldhall states, there were scores of houses once represented on the walls of the Hall.
Hawks and eagles, dragons and griffins, suns and stags, wolves and wyverns, manticores, bulls, trees and flowers, harps, spears, crabs and krakens, red lions and golden lions and chequy lions, owls, lambs, maids and mermen, stallions, stars, buckets and buckles, flayed men and hanged men and burning men, axes, longswords, turtles, unicorns, bears, quills, spiders and snakes and scorpions
A Dance With Dragons - ibid. A list of the houses can be found here
The house range from all over the realm and are not only made up of those of the northerners.
