When we read works in translation, it's vital to remember that every translation is also an interpretation. Every translation has weaknesses, but many also have great strengths, and the choice of a translation is, in many ways, a matter of taste. While I certainly have not sampled every translation of The Iliad, The Odyssey, and The Aeneid, the following are both excellent and easily accessible. I want to stress that there are other fine translations, though readers should be sure to find a poetic rather than a prose translation. And as is always the case with poetry, readers should read as much of the text out loud as possible.
Homer. The Iliad. Trans. Richmond Lattimore. Chicago: University of Chicago Press, 1951.
Homer. The Iliad. Trans. Robert Fagles. New York: Viking Penguin, 1990.
Homer. The Odyssey. Trans. Richmond Lattimore. New York: Harper & Row, 1965.
Homer. The Odyssey. Trans. Robert Fagles. New York: Penguin, 1996.
Virgil. Aeneid. Trans. Allen Mandelbaum. New York: Bantam Books, 1971.
Virgil. Aeneid. Trans. Robert Fagles. New York: Penguin, 2006.