While looking for such a basket, I stumbled upon Lantern Moon's even lovelier, to my eyes anyway, rice baskets from Vietnam. I decided to give the smallest one a try and, continuing the cautious streak, ordered a plain one.
It has since arrived and been in constant use. It is lightweight but strong and despite being the smallest one holds quite a lot: one almost complete TSJ (i.e., Toddler Suprise Jacket), two balls of yarn, the pattern, three magazines, and occasionally an ipod or even some toys. It is very pliable but keeps a nice, deep upright shape so your goods do not spill out and roll away.
Another perk is that, like a Transformer, the upper portion with the handles can tuck down into the bottom half so that it can be stored stacked, or filled like a bowl. This made me love it even more. I am trying to justify a second one!
I am sure they would be great for holding so many other things!