The Geometry of the Sphere by John Polking, Rice U., recounts the geometry of Girard's theorem, the relationship between angle sum of triangles and spherical area.
Spherical Geometry Demo, by John Sullivan, U. of Illinois, is a Java applet that demonstrates parallel transport and holonomy.
Kaleidotiles, by Jeff Weeks, shows tessellations of the sphere (and related polyhedra). It has a download site linked from this page at the Geometry Center.
The home page of David Henderson, the author of textbooks taking an investigative approach to spherical and other geometry, has a link to his bibliography of geometry books and some information about his text..
This course on Celestial Mechanics at the University of Sheffield has a chapter on Spherical Geometry, with topics:i. introduction ii. the geometry of the sphere iii. spherical trigonometry iv. position on the earth's surface v. example problems.
This page of Dave Rusin at Northern Illinois University has a number of practical methods for computing on the sphere.
The spherical Pythagorean Theorem is explained on this page at Harvey Mudd College.
The Math Forum is probably the best web math resource, including a page of links on Elliptical and Spherical Geometry. (By the way, Elliptical geometry is not geometry on an ellipsoid, it is a version of spherical geometry where a pair of opposite points counts as one point, so then two great circles intersect in one "point".)
A fascinating Java applet showing Stereographic projection is on a page of John Sullivan at UIUC.
Wilson Strothers's Page on Stereographic Projection and Inversion
Mathworld Page defining Stereographic Projection
Reference for Wulff nets and Crystallography
The Stereonet Technique Sections of the Structural
Geology Techniques course pages by Steven Dutch, Natural and Applied Sciences,
University of Wisconsin - Green Bay, has a number of interesting pages for geometry
and applications, including Spherical
Projections, Constructing
the Stereographic Projection,
How Spherical Projections are Used , Plotting
Objects on the Opposite Side of the Sphere, and a number of pages on using
stereographic projection in descriptive geometry.
International Union of Crystallography pamphlet on Stereographic Projection (other IUC pamphlets have math content also)
Stereographic projection of crystal faces
North Polar Stereographic projection of northern hemisphere
Wide-angle Imaging Geometry by Margaret M. Fleck
Proof that the Stereographic Projection of a Circle is a Circle
Coordinate description of Stereographic Projection from Geometry and the Imagination
Application of stereographic projection to MEIS (Medium Energy Ion Scattering )
A very good source for the geometry of cartography is the Cartography document of John Polking (in Adobe Acrobar format). Another page at Rice by high school teacher Cynthia Lanius brings together recourses for K12 students; the main page for this map site is at this link.
This site at U. Alberta has some history and a number of interesting references and a page with an interactive Java applet.
This page at UBC has some interesting figures. A history of math page at SFU has a summary of dates and accomplishments of mapmakers of the 1500s and other times.
An annotated bibliography of projections from Hunter.This Ask Dr. Math page explains how to map a point on the plane back to the sphere via Mercator projection.
This site of Hans Havlicek has an extensive gallery of maps of the earth by various projections. The Map Projection Overview of Peter Dana also has an interesting gallery.
For Unix fans, there is software: GMT Unix software for mapping with another site for GMT Help.
To go one step beyond, there is an animation of a Stereo projection of a 4D Cube.