Related is the math stackexchange question Book on coordinate transformations.
In two comments there I suggested looking at some of the many lengthy treatises on mathematical methods for physicists for beginning graduate students in physics, in particular Morse/Feshbach's 2-volume treatise Methods of Theoretical Physics. You can find reviews at amazon.com for Part I and Part II and Parts I & II.
Kris writes (in part) in a review at the "Parts I & II" page:
These books go into great detail on what are now considered esoteric coordinate systems (elliptical, parabolic, etc); this may be the best place to find material on this topic.
(ADDED A WEEK LATER) I happened to be at a university library this weekend and while there I looked at Morse/Feshbach. Pages 656-666 of Part I has summaries of the following:
Rectangular Coordinates, Circular Cylinder Coordinates, Elliptic Cylinder Coordinates, Parabolic Cylinder Coordinates, Spherical Coordinates, Conical Coordinates, Parabolic Coordinates, Prolate Spheroidal Coordinates, Oblate Spheroidal Coordinates, Ellipsoidal Coordinates, Paraboloidal Coordinates, Bispherical Coordinates, Toroidal Coordinates.