We present Johnson UBV, and Kron-Cousins I photometry for about 60,000 stars in a region of 44x33 arcmin$^2$ centered on the Galactic globular cluster (GGC) NGC 2808. The central rlt100 arcsec region has been mapped also in the F218W, F439W, and F555W bands with the HST WFPC2 camera. Overall, we cover a field which extends from the center to about 1.7 tidal radii. Photometric calibration has been secured by more than 1,000 standards, and the HST B and V photometry has been linked to the groundbased system. We confirm the anomalously elongated horizontal branch (HB) with gaps along it, and we show that the gaps are statistically significant. Most importantly, we find that: the extended blue tail of HB (EBT) is present beyond 400 arcsec, corresponding to more than nine times the half mass radius r_h, and extends to V=21.2 also in these external regions; also the gaps on the EBT are present at least out to 400 arcsec from the cluster center, and possibly beyond that. The location of the gaps in the HB seems to be the same all over the cluster. there are no significant radial gradients in the distribution of the stars in the different HB stumps and some marginal evidence of an increase in the number of red giant branch (RGB) stars in the cluster core. The observational facts presented in this paper seem to exclude the possibility that the EBTs originate from tidal stripping of the envelope of the RGB stars due to close encounters in high density environments or to mass transfer in close binaries. Also, it is not clear whether the presence of EBTs and gaps on them are the manifestation of the same physical phenomenon. We have also shown that the jump recently identified in the HB using Strömgren-u photometry is clearly visible also in the U, U-B plane, at T_e ~ 11,600 K. Finally, we present the luminosity function (LF) of the RGB. The LF clearly shows the presence of the usual RGB bump, but also a second feature, 1.4 magnitudes brighter in V, that we have named RGB heap. The RGB heap, visible also in other GGCs, is a new feature that, because of its position on the RGB, we have tentatively associated with the recently discovered K giant variables. Based on observations made at the European Southern Observatory, La Silla, Chile, and on observations with the NASA/ESA Hubble Space Telescope.