We report on the results of a three-year program of coordinated X-ray and optical monitoring of the narrow-line Seyfert 1 galaxy NGC 4051. The rapid continuum variations observed in the X-ray spectra are not detected in the optical, although the time-averaged X-ray and optical continuum fluxes are well correlated. Variations in the flux of the broad Hβ line are found to lag behind the optical continuum variations by 6 days (with an uncertainty of 2-3 days), and combining this with the line width yields a virial mass estimate of ∼1.1 × 10⁶ M_⊙, at the very low end of the distribution of active galactic nucleus masses measured by line reverberation. Strong variability of He II λ4686 is also detected, and the response time measured is similar to that of Hβ but with a much larger uncertainty. The He II λ4686 line is almost 5 times broader than Hβ, and it is strongly blueward asymmetric, as are the high-ionization UV lines recorded in archival spectra of NGC 4051. The data are consistent with the Balmer lines arising in a low-to-moderate-inclination disklike configuration and the high-ionization lines arising in an outflowing wind, of which we observe preferentially the near side. Previous observations of the narrow-line region morphology of this source suggest that the system is inclined by ∼50°, and if this is applicable to the broad Hβ-emitting region, a central mass of ∼1.4 × 10⁶ M_⊙ can be inferred. During the third year of monitoring, both the X-ray continuum and the He II λ4686 line went into extremely low states, although the optical continuum and the Hβ broad line were both still present and variable. We suggest that the inner part of the accretion disk may have gone into an advection-dominated state, yielding little radiation from the hotter inner disk.