This tutorial gives an overview of how to make a bunch of reusable fabric grocery bags for less than 2 dollars each. (And most of that cost is in the webbing for the handles. They'd cost less than 50 cents if you use denim from old jeans.)
Note (March 09)- I've been using these same bags for just under 2 years. We use them almost every single time we go to the grocery store. And we have 3 kids at home with us, so we shop a lot. We also use them for almost ALL of our errands... clothes shopping, library, even the hardware store. I also wash the bags pretty often. The point it, they have been used hard. Very hard. And even though they're made of fairly thin fabric (which is kind of the point, as I need to be able to cram all of them into their bag, week after week), none of them have ever torn. 
To make these, you need access to a sewing machine, but don't even need to sew all that straight. Remember, you just need to make them prettier than the ugly plastic things you're using now. How hard can that be?
-For my bags, I repurposed an old sheet that was in fairly good condition (not threadbare at all).
-I buy the sheets at the thrift store for between $2 and $4 each.
(The price has gone up since I originally posted. They're between $3 and $6 now. Still a good deal, though.)-I wash them in hot water before cutting.
-I've been able to get between 6 and 10 bags per sheet.
-Flat sheets are easiest, but fitted ones will work too. You'll just need to cut off the elastic (
click here to see how to reuse it).
-Cut as many 18" x 42" rectangles as you can from the sheet. (This results in a fairly big bag that's about 17 inches square. You can easily make it bigger or smaller, depending on your needs- and the size of your sheet. Regular plastic grocery bags are only about 11 by 13 inches. I'm thinking of making some more that are smaller and labeling the big ones with 'Light Items Only' because a big bag full of cans is way too heavy, but can be perfect for that jumbo sized toilet paper.)
-Basically, you're just sewing a very crude bag, with no lining. I kept it simple so I could make bunches of them. There's only one little trick that I figured out, shown in the next few pictures.
-Fold in half, wrong side together and pin like shown, about 3 inches from bottom.

Now, pull top down...

til it's even with the pins (creating a fold from pin to pin)...

grasp all four layers of fabric at pins...

and lift up. Then lay it back down flat.
Note- I just replied to a reader who had some confusion with this step. Here is the clarification I gave her "First of all, when you pull the top down, you’ll be pulling both corners of the front straight down till there is a fold right even with the pins. At this point, yes, you will have 3 layers, but when you pinch at the pins and lift up, the back of the bag will fall over your fingers and make four layers (you’ll have to reposition your fingers at this point). I actually fold the back layer down as I’m pinching, so that, in essence, I am grabbing four layers all at once."
-The wrong sides will now be facing out.

(This is much less complicated than it sounds. Thus all the pictures.)
-Sew up the sides. The third option on
this tutorial shows how to run both a straight stitch and a zig zag stitch in order to finish the edges nicely. Unfortunately, because of the folds in the seam, a French seam won't work here. The zig zag does the trick, though.
-If you want to check that you did this right, flip it right side out. It should look like this.

-Turn the bag back inside out and iron each seam to one side.
-Fold down top edge of bag about 1/4 inch and iron. (Ya, in these pictures the top of the bag is actually at the bottom of the picture.)

-Now fold the top down again about 2 inches. Iron.

-I pin in squares of scrap fabric to reinforce where the handles go (about 5 inches from the edge). You can use denim or canvas. Just make sure they're right up against the top fold so they get sewn in with the next seam.

-Now, sew two seams all the way around the top of the bag, one 1/4 inch seam parallel to the very top fold and one 1/4 inch up from the bottom fold.
-After that, you can turn it right side out and attach the handles.
-You can use webbing (like I did here) or
sew your own handles out of sturdy fabric. I fold the cut edge underneath to keep it from fraying. This step is probably the most difficult; keep with it, it just takes practice.

-Just make sure to keep the rest of the handle out from under the presser foot or you'll end up with this... I can't even tell you how often this happens to me.

-You can attach the handles to the inside or outside of the bag, depending on the look you prefer.

That's it. Please let me know if you have any questions. And I'd love to see any you make. There's even a
Flickr group to post pictures on.
One Note- if any men will ever be using these for shopping, you may want to consider doing these from a more masculine print. Jeff originally refused to bring the pretty blue and yellow flowered ones to the store, but has since gotten over it.
Oh yah, here's one last picture... of my grocery bag, bag. It's got a front pocket for the
Produce Bags and is closed using my Buffalo Scrunchy (cut off the fitted sheets).

This is basically sewn up with a channel like the
produce bags, but bigger and with a pocket.