Swift triggered on a precursor to the main burst of GRB 061121 (z=1.314), allowing observations to be made from the optical to gamma-ray bands. Many other telescopes, including Konus-Wind, XMM-Newton, ROTSE and the Faulkes Telescope North, also observed the burst. The gamma-ray, X-ray and UV/optical emission all showed a peak ~75s after the trigger, although the optical and X-ray afterglow components also appear early on - before, or during, the main peak. Spectral evolution was seen throughout the burst, with the prompt emission showing a clear positive correlation between brightness and hardness. The Spectral Energy Distribution (SED) of the prompt emission, stretching from 1eV up to 1MeV, is very flat, with a peak in the flux density at ~1keV. The optical-to-X-ray spectra at this time are better fitted by a broken, rather than single, power-law, similar to previous results for X-ray flares. The SED shows spectral hardening as the afterglow evolves with time. This behaviour might be a symptom of self-Comptonisation, although circumstellar densities similar to those found in the cores of molecular clouds would be required. The afterglow also decays too slowly to be accounted for by the standard models. Although the precursor and main emission show different spectral lags, both are consistent with the lag-luminosity correlation for long bursts. GRB 061121 is the instantaneously brightest long burst yet detected by Swift. Using a combination of Swift and Konus-Wind data, we estimate an isotropic energy of 2.8x10^53 erg over 1keV - 10MeV in the GRB rest frame. A probable jet break is detected at ~2x10^5s, leading to an estimate of ~10^51 erg for the beaming-corrected gamma-ray energy.