We aim to detect and identify the faint X-ray sources belonging to Galactic globular clusters in order to understand their role in the evolution of globular clusters. We present a new Chandra X-ray observation of the Galactic globular cluster NGC 2808. Previous observations with XMM-Newton and ultraviolet observations with the Hubble Space Telescope are re-investigated to help identify the Chandra sources associated with the cluster. From statistical analysis, 16 sources are very likely to be linked to NGC 2808. We found one likely neutron star low-mass X-ray binary in quiescence and 8 cataclysmic variable candidates in the core of NGC 2808. The other core sources are also cataclysmic variable candidates, but some of the faintest could possibly be chromospherically active binaries or millisecond pulsars. This significant population of close binaries is likely to play an important role in slowing down the core collapse of this cluster. We found 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. From X-rays and radio (ATCA) oobservations, we found no evidence of an intermediate mass black hole in NGC 2808 and derived mass constraints of several hundreds solar masses.