Here are a couple examples of oval mats. The left image shows a single mat. On the right is a double oval mat.
V-grooves are straight grooves (with a "V" cross section) cut in the face of a mat to add flair. Most mats have a white core, which would be exposed by the groove, but black-core mats are also available. To the left is an example of a single V-groove on a single mat. The right picture shows an example of a triple V-groove with off-set corners.
Another option is a stepped-corner mat. In groups they look like little stairs climbing each corner. The left picture shows a single step on a single mat. The right picture shows an example of a single step in a double mat. Double or triple steps, although not shown, are certainly possible.
Here are a couple more variations with double mats. The left image shows a double mat with a V-groove in the outer mat. This is pretty straight forward. On the right, the V-groove is on the inner mat. This is a little more complicated because it's tougher to line up correctly.
The image on the left shows an embellishment I put on a picture of a church. Below are a couple examples of more intricate mats. It is possible that the only impediment to mat design may be our own imaginations.
For the roadrunner picture on the left, the mat was inspired by the design of the New Mexico state flag, but has undergone a couple stages of abstraction. The mat on the right, though simpler, uses non-right angles on some cuts to complement the architectural drawing.