The Orion Nebula Cluster and the molecular cloud in its vicinity have been observed with the ACIS-I detector on board the Chandra X-ray Observatory with 23 hours exposure. We detect 1075 X-ray sources: 91% are spatially associated with known stellar members of the cluster, and 7% are newly identified deeply embedded cloud members. This provides the largest X-ray study of a pre-main sequence stellar population. We examine here the X-ray properties of Orion young stars as a function of mass. Results include: (a) the discovery of rapid variability in the O9.5 31 M_o star theta^2A Ori, and several early B stars, inconsistent with the standard model of X-ray production in small wind shocks; (b) support for the hypothesis that intermediate-mass mid-B through A type stars do not themselves produce significant X-ray emission; (c) confirmation that low-mass G- through M-type T Tauri stars exhibit powerful flaring but typically at luminosities considerably below the `saturation level; (d) confirmation that the presence or absence of a circumstellar disk has no discernable effect on X-ray emission; (e) evidence that T Tauri plasma temperatures are often very high with T >= 100 MK, even when luminosities are modest and flaring is not evident; and (f) detection of the largest sample of pre-main sequence very low mass objects showing high flaring levels and a decline in magnetic activity as they evolve into L- and T-type brown dwarfs.