Trajectory database (TD) management is a relatively new topic of database research, which has emerged due to the explosion of mobile devices and positioning technologies. Trajectory similarity search forms an important class of queries in TD with applications in trajectory data analysis and spatiotemporal knowledge discovery. In contrast to related works which make use of generic similarity metrics that virtually ignore the temporal dimension, in this paper we introduce a framework consisting of a set of distance operators based on primitive (space and time) as well as derived parameters of trajectories (speed and direction). The novelty of the approach is not only to provide qualitatively different means to query for similar trajectories, but also to support trajectory clustering and classification mining tasks, which definitely imply a way to quantify the distance between two trajectories. For each of the proposed distance operators we devise highly parametric algorithms, the efficiency of which is evaluated through an extensive experimental study using synthetic and real trajectory datasets.