The European Gaia astrometry mission is due for launch in 2011. Gaia will rely on the proven principles of the ESA Hipparcos mission to create an all-sky survey of about one billion stars throughout our Galaxy and beyond, by observing all objects down to 20 mag. Through its massive measurement of stellar distances, motions and multicolour photometry, it will provide fundamental data necessary for unravelling the structure, formation and evolution of the Galaxy. This paper presents the design and performance of the broad- and medium-band set of photometric filters adopted as the baseline for Gaia. The 19 selected passbands (extending from the UV to the far-red), the criteria and the methodology on which this choice has been based are discussed in detail. We analyse the photometric capabilities for characterizing the luminosity, temperature, gravity and chemical composition of stars. We also discuss the automatic determination of these physical parameters for the large number of observations involved, for objects located throughout the entire Hertzsprung-Russell diagram. Finally, the capability of the photometric system (PS) to deal with the main Gaia science case is outlined