It is his sister, Madeleine Usher. The wonderful thing about this story is that the house is also portrayed as a living, breathing entity. Once Roderick buries his sister, whom he has watched waste away until what he believes is her death, the house reacts! She has been buried alive, and as they attempt to get her out of the cript, the house begins to break apart. Only the narrator survives, and he watches the house fall into the crevice in the ground. So, the House of Usher has figuratively fallen with the deaths of Roderick and Madeleine, but it has also literally "fallen" to the ground.
Madeline Usher, Roderick's twin sister, is his only living relative. The two of them are actually the only surviving members of the Usher family.