We report on multi-wavelength observations, ranging from the X-ray to radio wave bands, of the IPN-localized gamma-ray burst GRB 070125. Spectroscopic observations reveal the presence of absorption lines due to O I, Si II, and C IV, implying a likely redshift of z = 1.547. The well-sampled light curves, in particular from 0.5 to 4 days after the burst, suggest a jet break at 3.7 days, corresponding to a jet opening angle of ~7.0 degrees, and implying an intrinsic GRB energy in the 1 - 10,000 keV band of around E = (6.3 - 6.9)x 10^(51) erg (based on the fluences measured by the gamma-ray detectors of the IPN network). GRB 070125 is among the brightest afterglows observed to date. The spectral energy distribution implies a host extinction of Av < 0.9 mag. Two rebrightening episodes are observed, one with excellent time coverage, showing an increase in flux of 56% in ~8000 seconds. The evolution of the afterglow light curve is achromatic at all times. Late-time observations of the afterglow do not show evidence for emission from an underlying host galaxy or supernova. Any host galaxy would be subluminous, consistent with current GRB host-galaxy samples. Evidence for strong Mg II absorption features is not found, which is perhaps surprising in view of the relatively high redshift of this burst and the high likelihood for such features along GRB-selected lines of sight. Comment: 50 pages, 9 figures, 5 tables Accepted to the Astrophysical Journal