The particle swarm optimization (PSO) technique is utilized to solve a variety of trajectory optimization problems. PSO is a stochastic global optimization method which relies on a group of potential solutions to explore the search space. Conceptually, each particle in the swarm utilizes its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on the optimal solution. It is relatively easy to implement, and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although PSO has been successfully employed in solving discrete optimization problems, its application in dynamic optimization, as posed in the Optimal Control Theory, has been little explored. In this work, we use PSO to generate near-optimal solutions to several non-trivial trajectory optimization problems, including thrust programming for minimum-fuel, multi-burn coplanar rendezvous, and computing the maximum altitude climb path for an aircraft. The control functions are assumed to be linear combination of B-Splines, the coefficients of which are selected by the swarm optimizer. A dynamic multi-stage-assignment penalty function is incorporated to enforce the associated constraints. Finally, for each of the test cases considered, the PSO solution is compared with its gradient-based counterpart.