There is no officially most famous sentence, but the most quoted lines of Machado de Assis are "To the victor, the potatoes," from Quincas Borba, and the one that closes The Posthumous Memoirs of Brás Cubas: "I had no children, and I passed on to no creature the legacy of our misery."
The first comes from chapter VI of Quincas Borba. The philosopher explains his doctrine with the image of two starving tribes and a potato field that feeds only one of them, and concludes: "To the vanquished, hatred or compassion; to the victor, the potatoes." The second is the last sentence of the book, in chapter CLX, "Of Negatives," in which the dead Brás Cubas takes stock of his life.
From Dom Casmurro, the most remembered is the description of Capitu's eyes. In chapter XXXII, "Olhos de ressaca" ("Undertow Eyes"), Bentinho recalls the definition given by the family dependent José Dias, "oblique and dissembling gypsy eyes," and then looks for his own image: "Eyes of undertow? Well, of undertow."
Another line from The Posthumous Memoirs of Brás Cubas, much repeated, comes from chapter XXIV: "frankness is the first virtue of a dead man."
On Clavis: The Posthumous Memoirs of Brás Cubas, Quincas Borba.