According to some, a fundemental question. Pragmatism and positivism would answer thusly: "it depends on how you define 'real.'" It really makes the question rather unimpressive.
For those who like word games, however, it's deeper than that triviality. Does the universe exist as matter, which I am able to perceive? Or is it rather my perceptions that are simply creations of my thought? Or are they really God's thoughts, that exist outside of the material realm?