Kreacher, of course, knew, but could not tell anyone in the family, and would not tell anyone out of it. Nevertheless quite a number of them know he's dead. Kreacher speaks so feelingly of his mother's grief, but not how she knew.
Some of them know he betrayed Voldemort and died as a consequence. How? Indeed, at one point, Lupin says that he only lasted three days after betraying Voldemort. But Sirius knows so little of it that he assumes it was panic, and Lupin seems to assume that Regulus was trying to hide (since he compares Karkaroff's lasting a year to those three days.)
And when Voldemort reappears in Goblet, he does not list among his Death Eaters one who betrayed him and died of it. Three who died in his service to be sure -- and while he perhaps omitted Regulus because they all knew what price he paid, and he's only discussing what happened since his fall -- there's the little matter of how he knows that Regulus is dead without knowing how. Because if he had known how, he would have reacted much sooner to the news; he reacted with alacrity in Hallows to the news of the raid on Gringotts. As Harry hears his thoughts, we know he had coped with the knowledge the diary was gone because it was an early venture. . . .
Mind you, magic that could conclusively tell you that someone was dead would be very useful indeed, and has a long tradition in fairy tales. And they do seem to have reliable info -- Moody can tell Harry that members of the Order of the Phoenix are dead even though the body was never found.
Magic that would conclusively tell you someone was a traitor would be even more useful, except that -- he's a traitor. And he's got magic, too. As Fudge observed, the biggest problem wizards have with the use of magic in war is that the other side has magic, too.