In a first course of general relativity, it is usually quite difficult for students to grasp the concept of a geodesic. It is supposed to be straight (auto-parallel) and yet it "looks" curved. In these situations, it is very useful to have some explicit examples available which show the different behaviour of geodesics. In this paper, we present "GeodesicViewer", an interactive tool for studying the behaviour of geodesics in many different spacetimes. The geodesics can be represented in several ways, depending on the spacetime in question. The use of a local reference frame and "Cartesian-like" coordinates helps the students to develop some intuition in various situations. We present the various features of "GeodesicViewer" in the form of readily formulated exercises for the students. (Contains 9 figures.)