Here, we have a system in place that includes composting by the municipality. We each were issued a huge green compost bin into which goes (if you don't keep a compost yourself) any scraps from vegetables, meat, fish, used cooking oils and other fats, boxboard (cereal boxes and the like), yard trimmings. They advise wrapping meat/fish scraps in one sheet of newspaper, or in a boxboard box. The municipality collects it every two weeks, and sells the compost. Along with that, a bluebag for milk cartons, glass and plastic containers, plastic bags, egg cartons, cans. Newspapers and corrugated cardboard tied in string separately. Green bag for what little garbage is left. Soft drink containers are returnable - we pay a deposit.
Grocery stores still have free plastic bags, but for several years also carry 99c cloth bags which fit the same bag holder at the checkout as the plastic ones do. The checkout people here seem better trained than those mentioned above - they are very careful usually with packing and distributing weight per bag. They also usually pack anything drippy or toxic in a plastic bag, so there are still enough bags for lining trash cans or whatever at home. Usually customers will do some of the packing to speed things up.
I've often had to carry my groceries a good distance, so i love the cloth bags - they're strong and have comfortable handles, long enough that you can even sling one over your shoulder if necessary.