A quantum particle observed on a sufficiently large space-time scale can be described by means of classical particle trajectories. The joint distribution for large-scale multiple-time position and momentum measurements on a nonrelativistic quantum particle moving freely in R' is given by straight-line trajectories with probabilities determined by the initial momentum-space wave-function. For large-scale toroidal and rectangular regions the trajectories are geodesics. In a uniform gravitational field the trajectories are parabolas. A quantum counting process on free particles is also considered and shown to converge in the large-space-time limit to a classical counting process for particles with straight-line trajectories. If the quantum particle interacts weakly with its environment, the classical particle trajectories may undergo random jumps.