Typical Noble Family House

In the A Song of Ice and Fire novels and accompanying short stories, websites and RPG sourcebooks, there are over 300 named noble houses of Westeros. All of these are sworn to the Great Houses.
However, George R.R. Martin has admitted that his system of nomenclature for noble Houses isn't very precise, as major and minor lords are both called simply "lords" (as opposed to differentiating between "duke" and "baron" etc.) Each of the constituent regions of the Seven Kingdoms has about a dozen or so major Houses, i.e. House Umber is sworn to House Stark, rules a large area of the North, and several minor Houses serve the Umbers. House Cassel, meanwhile, is a minor House, sworn directly to House Stark, which has no minor Houses serving it. Thus there are roughly about 100 or so major Houses in the Seven Kingdoms at any one time, and numerous minor Houses who in turn serve them (not all of whom have been named).

Noble Houses are, according to the World of Ice and Fire sourcebook, generally unique to Westeros. It seems that none of the great cultures of Essos organized their elites into Houses, with the possible exceptions of the culture of Slaver's Bay (in the books they are referred to as Houses, but as great families in the TV series) It is explicitly stated that the Valyrians did not, as Aegon the Conquerer had to design the trappings of a Westerosi Great House for the Targaryen family from scratch. This doesn't mean that Valyria or many of the Free Cities weren't organized around elite families, just that the power invested in such families was somewhat less official than in Westeros.
Some of the noble Houses have a marked propensity for physical traits which are passed down through the generations. Although no one in Westeros has a concept of "genetics" as such, it is sometimes understand that "the seed is strong" and that black hair tends to be a dominant trait over blonde hair. Some of the notable examples include:

House Baratheon - black hair, blue eyes, and square jaws
House Bolton - Black hair and eerie "ghost grey" eyes (somewhere between very pale blue and practically like dirty ice)
House Florent - large ears
House Lannister - curly blonde hair and green eyes
House Lannister of Lannisport - straight blonde hair and green eyes
House Martell - classic "Salty Dornish" features of olive skin, dark hair, and dark eyes.