DS9 suggests that the Houses are noble families, though, and a class of commoners exists outside the Houses but is as Klingon as any of the nobleKlingons.
Martok was low-born, but his having a House doesn't exactly go against the idea of Houses being the mark of nobility. He did ascend in social status, after all, through military service. That the House carries his name is an indication of sorts that it has a very short history...
There are several examples of Kingons referring to a small, non-noble House. The one that comes to mind is at the end of Sons of Mogh when Kurn becomes Rodek. Likewise, Grilka is from a small, relatively unknown House. So I don't think all Houses are noble, and the vast majority of Klingons are a part of a House even if its an insignificant one. In Soldiers of the Empire Jadzia makes a statement to Worf implying that having no House at all is something even the average Klingong would look down on ("how will the crew feel about serving under a man without a House?" Or something like that)