A lovely example surface from Topology. The horned sphere is a pathological embedding of a sphere into 3-space. See the wikipedia article for details.
I used full supports when printing this on my Makerbot. Separating the support material from the model was highly non-trivial!
Just (3/13/16) uploaded a new .stl with fixes for some issues with the polygon orientation on the meshes.
OpenSCAD is awesome! For this design I created a module (called "spin" in the file "surf_of_revolution.scad") that allows one to do some of the fancy things that can be done in the builtin function "linear_extrude," but in this case while creating a rotary extrusion. So for example a twist factor and a scale factor can be applied to the surface of revolution.