The Japanese govt in their attempt to reduce the problems with plastic shopping bags were promoting the use of large scarves for carrying shopping.
They refer to it as Furoshiki.
The scarves resemble large bandannas There are 8 standard sizes from 18 to 52 inches but usually they are about 30 inches square.
Of course you can make them any size you like.
The preferred cloth is either synthetic (nylon, rayon?) or silk because it is strong and the knots hold well.
They have some interesting ways to tie them into bundles.

These two sites are a brief introduction.
http://www.infomapjapan.com/hstore/200709-infospecial.phtml
http://www.env.go.jp/en/focus/attach/060403-5.html