The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.