Since so many places are not allowing the use of plastic bags, it's nice to be able to make your own tote bags from inexpensive materials. These two tutorials have some fun and fairly easy methods for doing that.
Here is a great little tutorial on how to use an ordinary, boring tote bag as the lining and handles of a pretty tote in your choice of fabric. This would also be a good way to make a stained or discolored tote look good again.
Betz White tells us how to do this, and it is pretty simple stuff - if your tote doesn't have a box bottom.
At the end of the tutorial Betz says that you can do this with box bottom totes as well but, in thinking about it, I'm pretty sure you'd need to add some extra fabric to the top if you are going to box the bottom. This might take some math so as not to end up with a shortage at the top edge.
Instructions on how to make boxed corners.
I don't have any totes to recover at the moment, but it would be an option to buy inexpensive, plain totes and use them for this purpose.
Here is a place where you may be able to find some inexpensive totes if you want to make a selection for yourself, for gifts or to use as gift bags for "wrapping" presents. Be sure to pay attention to what how they are made. Some of the totes here look like the flimsier "press fabric" that is not woven, but some kind of plastic product. If you want real fabric, make sure to find some that are made that way.
Here is a tutorial from The Sewing Dork on how to upcycle a thrift store pillow case (or one inherited or that you don't use) into a reusable grocery bag. You can also use fabric that you already own, which is even better since you won't be spending any more money. :-)
Note: the pocket is totally not necessary. Skip it if you don't want the hassle.