Cut the tile in half. This gives you a 1:2 proportion of 6x12-inch tiles. Perfect for running bond (brick) pattern or even fancy schmancy herringbone as shown in the image up top.
This idea works best when your kitchen or bath flooring is a DIY project, as the man-hours for cutting and laying the tile can really stack up. But if you're doing the job yourself and want to save on materials and not necessarily time, this is a great way to make your floors into something special! It requires renting a wet saw, but you would probably need the tool anyway for edging even if you were using simple square tiles.