Alternatives to Voronoi for procedural map generation

When I think back on my polygon map generator project from 2010, the word I associate most with it is voronoi. I used Voronoi diagrams for spacing the points and also for constructing polygons around those points. Seven years later, I'm revisiting this, looking at the ways in which Voronoi wasn't a perfect match for my needs, and looking for alternatives.

I made my own polygons from Delaunay triangles and plan to use this for a future procedural map generation project.