The possible existence of maximal or near-maximal lepton mixing constitutes an intriguing challenge for fundamental theories of flavor. 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 =1-2 sin(2) theta (ex) and quantify the present experimental status for \epsilon\<0.3. We show that both probabilities and observables depend on <epsilon> quadratically when effects are due to vacuum oscillations and they depend on epsilon linearly if matter effects dominate. The most important information on nu (e) mixing comes from solar neutrino experiments. We find that the global analysis of solar neutrino data allows maximal mixing with confidence level better than 99% for 10(-8) eV(2) less than or similar to Deltam(2) less than or similar to x 10(-7) eV(2). In the mass ranges Deltam(2)greater than or similar to1.5 x 10(-5) eV(2) and 4 x 10(-10) eV(2) less than or similar to Delta m(2) x 10(-7) eV(2) the full interval \epsilon\<0.3 is allowed within <similar to>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 similar to 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.