Plastic bags on their own aren't quite strong enough to hold anything too heavy (at least not for an extended period of time), but when broken down into "plarn" - plastic yarn - they can be woven into some very sturdy fabric.
This video teaches you how to make "plarn" for weaving. You can use this same exact technique for T-Shirts (except cut the strips 3/4").
Start with a plastic grocery/shopping bag. Fold and cut off the bottom and handles so that now you have only a tube. Fold one edge over leaving an edge of appx 3 ". Cut 1 1/2" strips in the folded edge. Open it up and then make the diagonal cuts for one continuous strip. This will yield appx 9 yards of "plarn".
You're now ready to weave some nice fabrics for tote bags, make up cases, maybe even a rain coat for your dog?
I have 2 projects posted at http://rigidheddleweaving.com for this fabric.