We use optical and near-infrared star counts to explore the structure and dynamics of the Orion Nebula Cluster. This very young (< 1 Myr) cluster is not circularly symmetric in projection, but is elongated north-south in a manner similar to the molecular gas distribution in the region, suggesting that the stellar system may still reflect the geometry of the proto-cluster cloud. Azimuthally-averaged stellar source counts compare well to simple spherically-symmetric, single-mass King cluster models. The model fits suggest that the inner Trapezium region should be regarded as the core of the Orion Nebula Cluster, not as a distinct entity as sometimes advocated. We estimate that the core radius of the cluster is 0.16-0.21 pc and that the central stellar density approaches 2 x 10^4 stars pc^{-3}. Adopting the stellar velocity dispersion from published proper motion studies, virial equilibrium would require a total mass within about 2 pc of the Trapezium of ~4500 M_sun, slightly more than twice the mass of the known stellar population, and comparable to the estimated mass in molecular gas projected onto the same region of the sky. If ~20% of the remaining molecular gas is converted into stars, thus adding to the binding mass, given that the present stellar population alone has a total energy close to zero, the ONC is likely to produce a gravitationally bound cluster. The ONC also exhibits mass segregation, with the most massive (Trapezium) stars clearly concentrated towards the center of the cluster, and some evidence for the degree of central concentration to decrease with decreasing mass down to 1-2 M_sun, as would be expected for general mass segregation. Given the extreme youth of the stars compared to the estimated range of collisional relaxation times, the mass segregation is unlikely the result of cluster relaxation. Instead, we suggest that the mass segregation reflects a preference for higher-mass stars to form in dense, central cluster regions.