  We present a detailed analysis of the zenith angle distributions of
atmospheric neutrino events observed in the Super-Kamiokande (SK) underground
experiment, assuming two-flavor and three-flavor oscillations (with one
dominant mass scale) among active neutrinos. In particular, we calculate the
five angular distributions associated to sub-GeV and multi-GeV \mu-like and
e-like events and to upward through-going muons, for a total of 30 accurately
computed observables (zenith bins). First we study how such observables vary
with the oscillation parameters, and then we perform a fit to the experimental
data as measured in SK for an exposure of 33 kTy (535 days). In the two-flavor
mixing case, we confirm the results of the SK Collaboration analysis, namely,
that \nu_\mu<--->\nu_\tau oscillations are preferred over \nu_\mu<--->\nu_e,
and that the no oscillation case is excluded with high confidence. In the
three-flavor mixing case, we perform our analysis with and without the
additional constraints imposed by the CHOOZ reactor experiment. In both cases,
the analysis favors a dominance of the \nu_\mu<--->\nu_\tau channel. Without
the CHOOZ constraints, the amplitudes of the subdominant \nu_\mu<--->nu_e and
\nu_e<--->\nu_\tau transitions can also be relatively large, indicating that,
at present, current SK data do not exclude sizable \nu_e mixing by themselves.
After combining the CHOOZ and SK data, the amplitudes of the subdominant
transitions are constrained to be smaller, but they can still play a
nonnegligible role both in atmospheric and other neutrino oscillation searches.
In particular, we find that the \nu_e appearance probability expected in long
baseline experiments can reach the testable level of ~15%.
