Context. Multiwavelength observations of gamma-ray burst prompt and afterglow emission are a key tool to separate the various possible emission processes and scenarios proposed to interpret the complex gamma-ray burst phenomenology. Aims. We collected a large dataset on GRB 060908 in order to carry out a comprehensive analysis of the prompt emission as well as the early and late afterglow. Methods. Data from Swift-BAT, -XRT and -UVOT together with data from a number of different ground-based optical/near-infrared and millimeter telescopes allowed us to follow the afterglow evolution after about a minute from the high-energy event down to the host galaxy limit. We discuss the physical parameters required to model these emissions. Results. The prompt emission of GRB 060908 was characterised by two main periods of activity, spaced by a few seconds of low intensity, with a tight correlation between activity and spectral hardness. Observations of the afterglow began less than one minute after the high-energy event, when it was already in a decaying phase, and it was characterised by a rather flat optical/near-infrared spectrum which can be interpreted as due to a hard energy-distribution of the emitting electrons. On the other hand, the X-ray spectrum of the afterglow could be fit by a rather soft electron distribution. Conclusions. GRB 060908 is a good example of a gamma-ray burst with a rich multi-wavelength set of observations. The availability of this dataset, built thanks to the joint efforts of many different teams, allowed us to carry out stringent tests for various interpretative scenarios, showing that a satisfactorily modelling of this event is challenging. In the future, similar efforts will enable us to obtain optical/near-infrared coverage comparable in quality and quantity to the X-ray data for more events, therefore opening new avenues to progress gamma-ray burst research.