  We study the phenomenological consequences of maximal and near-maximal mixing
of the electron neutrino with other ($x$=tau and/or muon) neutrinos. We
describe the deviations from maximal mixing in terms of a parameter
$\epsilon\equiv1-2\sin^2\theta_{ex}$ and quantify the present experimental
status for $|\epsilon|<0.3$. We find that the global analysis of solar neutrino
data allows maximal mixing with confidence level better than 99% for $10^{-8}$
eV$^2\lsim\Delta m^2\lsim2\times10^{-7}$ eV$^2$. In the mass ranges $\Delta
m^2\gsim 1.5\times10^{-5}$ eV$^2$ and $4\times10^{-10}$ eV$^2\lsim\Delta
m^2\lsim2\times10^{-7}$ eV$^2$ the full interval $|\epsilon|<0.3$ is allowed
within 4$\sigma$(99.995 % CL). We suggest ways to measure $\epsilon$ in future
experiments. The observable that is most sensitive to $\epsilon$ is the rate
[NC]/[CC] in combination with the Day-Night asymmetry in the SNO detector. With
theoretical and statistical uncertainties, the expected accuracy after 5 years
is $\Delta \epsilon\sim 0.07$. We also discuss the effects of maximal and
near-maximal $\nu_e$-mixing in atmospheric neutrinos, supernova neutrinos, and
neutrinoless double beta decay.
