We present an analysis of a 60-ks ROSAT X-ray observation of the Galactic open cluster NGC 2516, which has an age of about 110 Myr and a less than solar metallicity. 159 X-ray sources (0.5-2.0 keV) are found in the central portion of the Position Sensitive Proportional Counter (PSPC) together with six soft X-ray sources (0.1-0.4 keV). From the literature, we have constructed a uniform catalogue of photometrically selected cluster candidates. 65 of the X-ray sources are identified with photometric members of NGC 2516, and 25 X-ray sources are identified with probable cluster non-members or stars with no photometric measurements with which to assess cluster membership. The X-ray luminosity threshold is approximately 10^29 erg s^-1 and X-ray upper limits are determined for a further 136 possible cluster members. X-ray emission is observed across the Hertzsprung-Russell diagram, from spectral types of B2Ve to the early K stars which define the faintness limit of our optical catalogue. At least 73 X-ray sources have no plausible counterpart brighter than V=15. Some may be foreground or background stars, 10-15 are probably extragalactic, but the majority are likely to be lower mass stars in the cluster. Three of the soft X-ray sources are probable hot white dwarfs in binary systems with late-type stars. One of these may be in the cluster, the other two are foreground objects. X-ray emission from the hottest star in the cluster is attributed to a shocked stellar wind. 20 per cent of late B- and A-type stars are detected, which is consistent with the X-ray emission being the result of unresolved late-type companions. At least four out of the six magnetic, chemically peculiar stars are X-ray sources. We conclude that this is probably intrinsic, although an explanation involving binary companions cannot be entirely ruled out. Many F, G and K stars are detected, presumably as a result of dynamo-generated coronal activity. The peak level of X-ray activity is reached among the late G stars, which have an X-ray to bolometric flux ratio of 10^-3. This suggests that these stars have not yet spun down below the empirical X-ray saturation rotation speed of 10-20 km s^-1. Interpretation of the late-type star X-ray luminosity functions is hampered by the fact that there are likely to be contaminating field stars among the X-ray upper limits. The U-B, B-V colour-colour diagram for X-ray-selected cluster members reveals an ultraviolet excess among the F and G stars of NGC 2516, which is best explained by a less than solar metallicity, [Fe/H]=-0.32+/-0.06. Comparison with younger and older clusters shows that the late-type stars in NGC 2516 do not simply obey the widely accepted rotation-activity-age paradigm. We suggest a modification to the paradigm which explains the observations in terms of the different convection zone properties that late-type stars of differing metallicities have at the same colour or mass.