The BL Lac object 3C 66A was the target of an extensive multiwavelength monitoring campaign from 2003 July through 2004 April (with a core campaign from 2003 September to 2003 December) involving observations throughout the electromagnetic spectrum. Radio, infrared, and optical observations were carried out by the WEBT-ENIGMA collaboration. At higher energies, 3C 66A was observed in X-rays (RXTE), and at very high energy (VHE) in γ-rays (STACEE, VERITAS). In addition, the source has been observed with the VLBA at nine epochs throughout the period 2003 September to 2004 December, including three epochs contemporaneous with the core campaign. A gradual brightening of the source over the course of the campaign was observed at all optical frequencies, culminating in a very bright maximum around 2004 February 18. The WEBT campaign revealed microvariability with flux changes of ~5% on timescales as short as ~2 hr. The source was in a relatively bright state, with several bright flares on timescales of several days. The spectral energy distribution (SED) indicates a νFν peak in the optical regime. A weak trend of optical spectral hysteresis with a trend of spectral softening throughout both the rising and decaying phases has been found. On longer timescales, there appears to be a weak indication of a positive hardness-intensity correlation for low optical fluxes, which does not persist at higher flux levels. The 3-10 keV X-ray flux of 3C 66A during the core campaign was historically high and its spectrum very soft, indicating that the low-frequency component of the broadband SED extends beyond ~10 keV. No significant X-ray flux and/or spectral variability was detected. STACEE and Whipple observations provided upper flux limits at >150 and >390 GeV, respectively. The 22 and 43 GHz data from the three VLBA epochs made between 2003 September and 2004 January indicate a rather smooth jet with only very moderate internal structure. Evidence for superluminal motion (8.5+/-5.6 h-1 c) was found in only one of six components, while the apparent velocities of all other components are consistent with 0. The radial radio brightness profile suggests a magnetic field decay ~r-1 and, thus, a predominantly perpendicular magnetic field orientation. For questions regarding the availability of the data from the WEBT (Whole Earth Blazar Telescope) campaign presented in this paper, please contact the WEBT president Massimo Villata at villata [at] to.astro.it (villata[at]to[dot]astro[dot]it).