Aims: Using new Chandra X-ray observations and existing XMM-Newton X-ray and Hubble far ultraviolet observations, we aim to detect and identify the faint X-ray sources belonging to the Galactic globular cluster NGC 2808 in order to understand their role in the evolution of globular clusters. Methods: We present a Chandra X-ray observation of the Galactic globular cluster NGC 2808. We classify the X-ray sources associated with the cluster by analysing their colours and variability. Previous observations with XMM-Newton and far ultraviolet observations with the Hubble Space Telescope are re-investigated to help identify the Chandra sources associated with the cluster. We compare our results to population synthesis models and observations of other Galactic globular clusters. Results: We detect 113 sources, of which 16 fall inside the half-mass radius of NGC 2808 and are concentrated towards the cluster core. From statistical analysis, these 16 sources are very likely to be linked to the cluster. We detect short-term (1 day) variability in X-rays for 7 sources, of which 2 fall inside the half-mass radius, and long-term (28 months) variability for 10 further sources, of which 2 fall inside the half-mass radius. Ultraviolet counterparts are found for 8 Chandra sources in the core, of which 2 have good matching probabilities and have ultraviolet properties expected for cataclysmic variables. We find one likely neutron star-quiescent low-mass X-ray binary and 8 cataclysmic variable candidates in the core of NGC 2808. The other sources are cataclysmic variable candidates, but some could possibly be active binaries or millisecond pulsars. We find a possible deficit of X-ray sources compared to 47 Tuc which could be related to the metallicity content and the complexity of the evolution of NGC 2808. Table 1 is only available in electonic form at http://www.aanda.org