This paper explores trajectory options for the human exploration of Mars, with an emphasis on conjunction-class missions. Conjunction-class missions are characterized by short in-space durations with long surface stays, as opposed to the long in-space durations and short surface stays characteristic of opposition-class missions. Earth-Mars and Mars-Earth trajectories are presented across a series of mission opportunities and transfer times in order to explore the space of possible crew and cargo transfer trajectories. In the specific instance of crew transfer from Earth to Mars, the potential for aborting the mission without capture into Mars orbit is also of interest. As such two additional classes of trajectories are considered: free-return trajectories, where the trajectory would return the crew to Earth after a fixed period of time; and propulsive-abort trajectories, where the propulsive capability of the transfer vehicle is used to modify the trajectory during a Mars swing-by. The propulsive requirements of a trajectory, due to their associated impact on spacecraft mass, are clearly of interest in assessing trajectories for human Mars missions. Beyond the propulsive requirements, trajectory selection can have a significant impact on the entry velocity and therefore the aeroassist system requirements. The paper suggests potential constraints for entry velocities at Earth and Mars. Based upon Mars entry velocity, the 2-year period free-return abort trajectory is shown to be less desirable than previously considered for many mission opportunities.