This paper is aimed at obtaining a better understanding of driving behavior on horizontal curves of two-lane rural highways in terms of trajectories in relation to the different curve radii and directions by a driving simulator experiment. The driving simulator experiment involved 50 drivers and eight classes of curve radii, ranging from 125 m to 800 m. Overall, 2000 curve trajectories were analyzed and classified. Six major classes were defined: (1) ideal behavior, (2) normal behavior, (3) driving close to the centerline, (4) driving outside in curve approach, (5) cutting, and (6) correcting. Furthermore, 21 sub-classes were introduced to consider both lane departures and location of the corrective actions. The CATANOVA tests and Bhapkar’s tests showed that both the curve radius and the curve direction had a significant effect on the classification results. To get a clearer understanding of the effect of the curve radius and direction on curve negotiation, three macro-classes corresponding to safe, intermediate, and dangerous behavior were introduced. The safest behaviors significantly increased with the curve radius while the most dangerous behaviors significantly decreased with the curve radius. Furthermore, left curves showed a higher proportion of dangerous trajectories. Overall, it seems that the driving trajectories are a promising surrogate measure of safety as highlighted by the correlation between the trajectories identified as dangerous and the radii of the curves.