We search for the flavor-changing neutral current decays D-0 -> mu(+)mu(-) and D-0 -> e(+)e(-), and for the lepton-flavor violating decays D-0 -> e(+/-)mu(-/+) using 660 fb(-1) of data collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We find no evidence for any of these decays. We obtain significantly improved upper limits on the branching fractions: B(D-0 -> mu(+)mu(-)) < 1.4 x 10(-7), B(D-0 -> e(+)e(-)) < 7.9 x 10(-8), and B(D-0 -> e(+)mu(-)) + B(D-0 -> mu(+)e(-)) < 2.6 x 10(-7) at 90% confidence level.