  The Daya Bay and RENO reactor neutrino experiments have revealed that the
smallest neutrino mixing angle is in fact relatively large, i.e., theta_13 ~ 9
degrees. Motivated by this exciting progress, we perform a systematic study of
the neutrino mass matrix M_nu with one or two texture zeros, in the assumption
that neutrinos are Dirac particles. Among fifteen possible patterns with two
texture zeros, only three turn out to be favored by current neutrino
oscillation data at the 3 sigma level. Although all the six patterns with one
texture zero are compatible with the experimental data at the 3 sigma level,
the parameter space of each pattern is strictly constrained. Phenomenological
implications of M_nu on the leptonic CP violation and neutrino mass spectrum
are explored, and the stability of texture zeros against the radiative
corrections is also discussed.
