GRB 080810 was one of the first bursts to trigger both Swift and the Fermi Gamma-ray Space Telescope. It was subsequently monitored over the X-ray and UV/optical bands by Swift, in the optical by Robotic Optical Transient Search Experiment (ROTSE) and a host of other telescopes, and was detected in the radio by the Very Large Array. The redshift of z = 3.355 +/- 0.005 was determined by Keck/High Resolution Echelle Spectrometer (HIRES) and confirmed by RTT150 and NOT. The prompt gamma/X-ray emission, detected over 0.3-10 3 keV, systematically softens over time, with Epeak moving from 600 keV at the start to 40 keV around 100 s after the trigger; alternatively, this spectral evolution could be identified with the blackbody temperature of a quasi-thermal model shifting from 60 to 3 keV over the same time interval. The first optical detection was made at 38 s, but the smooth, featureless profile of the full optical coverage implies that this is originated from the afterglow component, not from the pulsed/flaring prompt emission. Broad-band optical and X-ray coverage of the afterglow at the start of the final X-ray decay ( 8 ks) reveals a spectral break between the optical and X-ray bands in the range of 1015-2 x 1016 Hz. The decay profiles of the X-ray and optical bands show that this break initially migrates blueward to this frequency and then subsequently drifts redward to below the optical band by 3 x 105 s. GRB 080810 was very energetic, with an isotropic energy output for the prompt component of 3 x 1053 and 1.6 x 1052 erg for the afterglow; there is no evidence for a jet break in the afterglow up to 6 d following the burst.