  The characteristic feature of the Kepler Problem is the existence of the
so-called Laplace--Runge--Lenz vector which enables a very simple discussion of
the properties of the orbit for the problem. It is found that there are many
classes of problems, some closely related to the Kepler Problem and others
somewhat remote, which share the possession of a conserved vector which plays a
significant r\^ole in the analysis of these problems.
