I have used those in the past as canvas for pictures, either painted, decoupaged or whatever appeals. I also have a few that I have waiting to be used where I have applied drywall compound in rough strokes.

Could the cork backing be used as a bulletin board?

Cut them into coasters.

Sand down the decorated side, and redecorate with paint, rubber stamps, stencils, collage - whatever you prefer. Seal with protective coating. Keep on using as coasters or placemats, or attach to the wall in a room: they will help act as soundproofing. Or glue flat magnets onto the back. Or use two the same size as covers for a home-made book; cut heavy weight paper the same size and decorate. Bind the book by punching or drilling holes into the covers and paper and weaving cord or ribbon through, or use key ring loops.

Give the repurposed coasters and placemats away as gifts.

Cutting boards for artists: they always need cork mats when cutting paper, etc for their work and those boards are usually very expensive to buy.

I can’t see if all are the rigid type, but if you have the kind that can be cut easily, you could make them fit into the bottom of a canvas shopping bag. They would ad shape and can be easily wiped off. The cork ones could be cut to fit under a house plant plate to keep it from marking the table surface. The small coasters might be fun to glue into a box, with a cloth ring top.

You can also check with local veterinary offices, they use place mats under food dishes in cages.

cover with felt and make some felt animal shapes or obects for kids to use as a story board. or paint with chalk board paint and put with some 25c chalk for kids at christmas/birthdays.