Plastic bags (thin type grocery bags) have been banned here in South Australia for at least 12 months. Shopping centres stock the "cloth" bags that you can buy for $1, if you forget your own.
Drawback is that now we need to actually purchase bin liners.
Strangely, the heavy duty plastic bags you get from department stores aren't banned.
Biodegradeable bags seem to be knackered before you even get to use them.