I'm in the same situation with a ton of 4x4" white tiles!

Coasters, magnets, small "backsplash" for sink if you don't have enough for a full size. Whatever you do, you want to paint them first. I would think regular acrylic paint and a good couple of layers of varnish (glossy) to seal them will do.

For the coasters, you can purchase, cut into smaller pieces and glue to the bottom of the tiles those round cork planter bottoms sold in garden sections of stores or garden centers. They go under the plants on porches or inside to absorb the water.

For the magnets, craft stores and maybe the "handyman" sections of bigger stores sell magnet strips that can be cut and all you do is peel and stick. I'd probably had some crazy glue to them for extra because of the weight of the tiles.

For the backsplash, you could create a painted scene and then make that the focal/center area of a larger backsplash area. Just don't forget to varnish it so the image doesn't rub off due to watersplash. You could use this same idea if you ever decide to retile a shower wall.

You could also use them as the sides of a wooden box that they'll fit onto. Paint an image, seal, and then glue them onto the sides of the box.

Hope these give you some ideas!