This thesis deals with the optimization of the ascent trajectories for single-stage suborbital (SSSO), single-stage-to-orbit (SSTO), and two-stage-to-orbit (TSTO) rocket-powered spacecraft. The maximum payload weight problem has been solved using the sequential gradient-restoration algorithm. For the TSTO case, some modifications to the original version of the algorithm have been necessary in order to deal with discontinuities due to staging and the fact that the functional being minimized depends on interface conditions. The optimization problem is studied for different values of the initial thrust-to-weight ratio in the range 1.3 to 1.6, engine specific impulse in the range 400 to 500 sec, and spacecraft structural factor in the range 0.08 to 0.12. For the TSTO configuration, two subproblems are studied: uniform structural factor between stages and nonuniform structural factor between stages. Due to the regular behavior of the results obtained, engineering approximations have been developed which connect the maximum payload weight to the engine specific impulse and spacecraft structural factor; in turn, this leads to useful design considerations. Also, performance sensitivity to the scale of the aerodynamic drag is studied, and it is shown that its effect on payload weight is relatively small, even for drag changes approaching ±50%. The main conclusions are that: the design of a SSSO configuration appears to be feasible; the design of a SSTO configuration might be comfortably feasible, marginally feasible, or unfeasible, depending on the parameter values assumed; the design of a TSTO configuration is not only feasible, but its payload appears to be considerably larger than that of a SSTO configuration. Improvements in engine specific impulse and spacecraft structural factor are desirable and crucial for SSTO feasibility; indeed, it appears that aerodynamic improvements do not yield significant improvements in payload weight.