We present the results of an eye tracking study that compares different visualization methods for long, dense, complex, and piecewise linear spatial trajectories. Typical sources of such data are from temporally discrete measurements of the positions of moving objects, for example, recorded GPS tracks of animals in movement ecology. In the repeated-measures within-subjects user study, four variants of node-link visualization techniques are compared, with the following representations of directed links: standard arrow, tapered, equidistant arrows, and equidistant comets. In addition, we investigate the effect of rendering order for the halo visualization of those links as well as the usefulness of node splatting. All combinations of link visualization techniques are tested for different trajectory density levels. We used three types of tasks: tracing of paths, identification of longest links, and estimation of the density of trajectory clusters. Results are presented in the form of the statistical evaluation of task completion time, task solution accuracy, and two eye tracking metrics. These objective results are complemented by a summary of subjective feedback from the participants. The main result of our study is that tapered links perform very well. However, we discuss that equidistant comets and equidistant arrows are a good option to perceive direction information independent of zoom-level of the display.