I've taken my long but too-skinny-to-use strips, about 3/4" wide, and used them to tie up my tomatos. I've also used them to make a sort of trellis for peas and pole beans. Gives a sort of calico garden effect!
One year I even made an edging for the garden out of the cardboards... free, versus buying landscape timbers... but they do sag after many rains. Next year I'm thinking of using them to make the paths in the vegetable garden. Anything that reduces weeding is fine with me!