Self-assembly of symmetric diblock copolymers confined in spherical nanopores is studied using simulated annealing Monte Carlo simulations. The dependence of the self-assembled morphologies and chain conformations on the degree of confinement and the strength of the surface interactions is examined systematically. A rich variety of novel structures under the three-dimensional confinement has been revealed. As the strength of the surface preference is increased gradually from neutral to weakly preferential and finally strongly preferential to one of the blocks, the observed sequence of stable structures is from perpendicular lamellae to helices and/or embedded structures and finally to concentric-spherical lamellae. As the degree of confinement decreases, the stable region of the concentric-spherical lamellae becomes larger, while that of the embedded structures becomes smaller. For the structures obtained in spherical nanopores, corresponding counterparts in two-dimensional (2D) confined systems can be identified. On the other hand, the chain conformations of the three-dimensional (3D) confined structures are different from that of their corresponding 2D counterparts. A model is proposed which gives a reasonable description for the layer thicknesses of the concentric-lamellae in both 3D and 2D confined systems. Furthermore, in the limit of large pores, the model predictions for 3D and 2D confined systems are consistent with that observed in one-dimensional confined systems.