For example, what about ND filters that work opposite to vignetting where the centre is darker than the outside?
These exist, they're called center-spot filters and are pretty common in the large-format world. They don't make much sense for SLR lenses though, because to be useful they have to be lens-specific and besides most SLR lenses don't have much vignetting (not nearly as much as wideangle LF lenses, anyways).
Or what about an ND filter where there's a single strip across the centre that is darker?
Singh-Ray has some "reverse grad" filters that are similar to what you describe, with the darkest portion in the center and then getting gradually lighter towards the edge. Useful for shooting with the sun close to the horizon so that you don't over-darken the sky above.
What other variations on ND filters are worthwhile?
Honestly I don't find ND filters useful at all for digital, and never use them. Some will argue that "getting it right in the camera" in one shot is ideal, but the truth is digital blending of bracketed shots can usually produce better results because you're not limited to having a straight-line boundary with a uniform transition from light to dark. There are just too many compositions where the grad filter will darken things that shouldn't be darkened and the result look unnatural.