A crochet "holdall" or "tote" made in dishcloth cotton (subsequently re-branded craft cotton). This one is lined and the craft cotton is soft and flexible. You could make it from a coarser type of jute, (I would use a larger hook), and leave it unlined, to use as a vegetable or market bag. I have also seen some excellent bags and bowls made from Herdwick yarn; these are crocheted very tightly to create a rigid fabric so the bags will keep their shape unsupported.
The bag is made in one piece starting at the base, and the straps are then attached separately.
Start at the base and make 21 ch.
1st round: Work 3 dc into 2nd ch
from hook; 1 dc in each of next 18 ch; work 3 dc into last ch; then continue
along other side of ch by working 1 dc in next 18 ch; join with slip stitch
to first dc of round. [42 sts]
Increase round: (inc1, 8 dc) 8 times. [80 sts]
Work in ridge pattern as follows:-
1st round: Work 1 dc in each dc.
Repeat last 2 rounds until work measures 11½ ins. from the the first
ridge worked at completion of base.
Straps (Make 2)
Make 49 ch and work in rows.
1st row: 1 dc in 2nd ch from hook,
1 dc in next 47 ch , I ch , turn.
To Make Up:
Cut piece of card to fit base.
Cut lining, 18 x 24 inches (this lines the depth of bag and allows for gathered top as well).
From remainder of material, cut two strips for lining handles, 15 x 2 inches, and for base, draw round the card shape on material and cut out about 1 in. away from pencil outline.
Cover one side of card with lining, folding over and sticking surplus
material onto the other side.
Join the 2 side edges of lining to make a tube.
Top Finish: Fold over top edge of lining to wrong side to make
3½ inch hem, and stitch in position. ¼ inch down from top folded
edge. make 2 rows of stitching, ½ inch apart, for draw-string. Open
seam between the 2 rows and insert tape.
Slip lining into bag and stitch into position by catching the 3½ inch hemline behind crochet (about ½ inch down from top of edge of crochet).
Catch lining to base.
Line handles and stitch on each side of bag.
Draw up tape and tie.
2 x 4oz. hanks Dishcloth Cotton.
ch: = chain
3 stitches to 1 inch in width.
Depth: 11½ inches; Oval base: 9½ x 4½ inches.
A Word on the Wool
There are a number of brands sold as "dishcloth cotton" or "craft cotton" but it's a little pot luck with the thickness - you will have to experiment with the tension and how you want the bag to look. You are looking for an Aran weight yarn with a yardage of about 75m to 50g.
Lion Brand Cotton is fairly common in the US and would be suitable if you can obtain it (and comes in exciting colours too...).
You can literally use balls of string for this kind of bag but I've always found that works out surprisingly expensive.