Fruit and vegetables don't need to be wrapped in protective packaging as long as you are careful when you transport them home. You'll quickly forget how nice a product's packaging looks on the shop shelf once you've opened it and put all of the plastic in the bin.
Supermarkets give away about 8 billion plastic bags each year. The vast majority of these go straight in the bin when you get home. However, you can help to prevent this build up of discarded plastic by bringing your own bags every time you shop. Nowadays shops are starting to charge for their plastic bags, so bringing your own may also save you money.