I always cut off and save the ends if I am cutting up a tie for patchwork.  In a quilt, these can be used as a prairie point-like addition.  I've used them in the corners, tucked into the binding; as a finish at the bottom of small quilts instead of binding that edge, tucked into the seams of a 4-patch like a windmill; and other places you might use a prairie point.  In clothing, they make great embellishments - cut them fairly small to tuck in seams.  I've also used one as a pocket flap on a vest pocket.