According to the Ouya Kickstarter page, an HD remake of Final Fantasy III will be a launch title for the Ouya. Or, more specifically, the Ouya Final Fantasy III "will be updated to exploit OUYA’s high-definition resolution in glorious graphic detail."
Final Fantasy III has been remade several times, most recently on the Nintendo DS—which included new 3D graphics and all new cinematic cut scenes—and on iOS. So hey, what's one more remake for the upcoming Android-based console?
There is no set release date yet for the Ouya, but it's expected to land in early 2013.