Order types are a means to characterize the combinatorial properties of a
finite point set in the plane. In particular, the crossing properties of all
straight-line segments spanned by a point configuration are reflected by its
order type. We establish a complete and reliable data base for all different
order types of size up to
. To the best of our knowledge, such a project
has not been carried out before, not even for point sets of smaller size. We
discuss several applications of this data base and related techniques to
prominent problems in computational and combinatorial geometry. These include
problems on crossing-free graphs like triangulations or simple
polygonalizations, but also general crossing problems like the rectilinear
crossing number.