What types of stencils are widely used?

I am working on a self-directed project for school. I am benchmarking optimization techniques of various stencil operations to determine an upper bound of their effectiveness, as a function of problem dimensionality, etc. To make my work more relevant, I would like to make sure that I am considering the “important” types of stencil.

I know that square stencils of various sizes are widely used in image processing, and that on-axis stencils of various sizes are used for scientific computing / PDE’s. I have also seen 3x3x3 cubical stencils used in CFD.

What other sorts of stencils are either widely used, or are edge-cases that are important to consider?