I've used cloth bags since Aldi opened. Don't get me wrong, I too use plastic bags for bin liners, but the come from other stores (fruit and veg, butcher, department stores) or they're given to me.
I also use cloth bags I've made. They're easy, cheap and usually very sturdy. Buy the calico or denim or homespun on sale, or recycle it from shirts, jeans, skirts, dresses you no longer wear to save money.
You can buy plain calico totes at craft stores, they're not expensive, if you don't think you can make them.
Here are the instructions for a couple of bags I made a couple of years ago. The instructions use bought bags, but by all means make them if you can.
Calico or plain coloured cotton tote
A picture to fit the tote
Iron-on transfer paper*
Step 1. Wash and dry your bag. I like to pre-wash the bags so that if they shrink they'll do so before the transfer is applied. Iron it.
Step 2. Find an image to use as the transfer. I found this image here: http://www.freeprettythingsforyou.com/ Make sure it is going to fit onto your tote. I usually print the image then use it as a template to work out the placement of the actual transfer.
Step 3. Follow the instructions on your transfer paper to print then apply the transfer to your tote.
And voila - in around 30 minutes (more if you can't make up your mind about the image) you have a lovely and unique tote to use or give as a gift for around $6.
*Spotlight and Lincraft sell iron-on transfer paper, but it's expensive. Buy it on sale (at least 40% off to make it cheap enough). You can also get it at Officeworks, where the packs are bigger, bringing the price per sheet down. Again, wait for a sale if you can. I have found it in some $2 shops too and it seems to be just as good a quality for a fraction of the price.