What kinds of data other than geographical are topologically spherical?
Any data consisting of a three element vector of numbers  $v =\{x,y,z\}$ could be viewed as topologically spherical if, after converting to polar coordinates, there is only one datum for every value of the 3D angle $\theta$. Thus, every point in the data represents an exterior of a topological sphere. This is taking the term "topological" literally and formally.

There are also graph structures (acyclic) that have neighborhood structures that allows the graph to be mapped topologically to a sphere. For example, all graphs that can be mapped to Platonic Solids (i.e. vertexes to vertexes, edges to edges, 1:1) are topological spheres. This can include irregular neighborhood structures, too.

As far as practical examples of these, none come to mind immediately.