Given a polygonal object (simple polygon, geometric graph, wire-frame, skeleton or more generally a set of line segments) in three-dimensional Euclidean space, we consider the problem of computing a variety of "nice" parallel (orthographic) projections of the object. We show that given a general polygonal object consisting of n line segments in space, deciding whether it admits a crossing-free projection can be done in O(n 2 log n + k) time and O(n 2 + k) space, where k is the number of edge intersections of forbidden quadrilaterals (i.e., a set of directions that admits a crossing) and varies from zero to O(n 4 ). This implies for example that, given a simple polygon in 3-space, we can determine if there exists a plane on which the projection is a simple polygon, within the same complexity. Furthermore, if such a projection does not exist, a minimum-crossing projection can be found in O(n 4 ) time and space. We show that an object always admits a regular projection (of interest to knot theory) and that such a projection can be obtained in O(n 2 ) time and space or in O(n 3 ) time and linear space. A description of the set of all directions which yield regular projections can be computed in O(n 3 log n + k) time, where k is the number of intersections of a set of quadratic arcs on the direction sphere and varies from O(n 3 ) to O(n 6 ). Finally, when the objects are polygons and trees in space, we