What's the fastest way, without using Python, to select every other vertex of an edge ring with an even number of verts?
In edit mode with entire edge ring selected:
Select> Checker Deselect
This should deselect every other vertex.
You can then use the 'offset' value in the toolshelf if you want the other vertices in the edge ring selected.
Offset by 1:
Note: This works in edge and face mode too, deselecting alternate edges or faces to get a checkerboard selection.