There is no single practice that is used across the board to prolong the shelf life of fruits and vegetables. Prior to 1986, especially in salad bars, it was very common practice to prolong the shelf life of fresh fruits and vegetables with sulfites. However, in that year, the U.S. Food and Drug Administration determined that sulfiting agents were no longer "considered GRAS" (Generally Recognized As Safe) for use with "fruits or vegetables intended to be served raw to consumers or to be presented to consumers as fresh." Dried fruits are still widely preserved in this way, however.
You've probably noticed more and more use of water sprays in grocery stores in recent years. These water sprays are not only designed to help provide the fruits and vegetables with a look of freshness but also to help preserve them from damage by microorganisms. It turns out that everyday, chlorinated water can help protect fresh fruits and vegetables from spoilage by bacteria and other organisms. This process also prolongs shelf life, since all we mean by "shelf life" is really prevention of spoilage. I don't have a problem with prevention of spoilage through water spraying, provided you take the time to rinse the produce at home (preferably with filtered water, and using a natural bristle brush when appropriate).
For some foods, early harvest and controlled ripening is another means of extending shelf life. Controlled use of a ripening agent like ethylene is popular with foods like bananas and tomatoes. Instead of harvesting these foods at a fully ripe stage, harvesting is done early on, when the foods are still green. The unripened foods can be transported and prepared for sale without continuing to ripen and lose shelf life. Then at some point in time closer to actual sale, the ripening agent, usually ethylene, will be sprayed onto the foods to trigger ripening. In addition to bananas and tomatoes, many other foods—including mangos, avocados, papayas, and persimmons—can have their shelf life partly regulated in this way.
Ethylene spraying is allowed by the National Organics Program for use on tropical fruits certified as organic, including bananas, pineapples, and mangos. I've read through the debate over this practice and believe that even though it's not the most desirable production method for these foods, there is limited risk from a health standpoint and that organic bananas, pineapples, mangos, and other fruits ripened in this way can still make nourishing additions to a Healthiest Way of Eating. From an environmental standpoint, however, I'd like to see this practice changed over time.
There's also waxing. Commonly waxed fruits and vegetables include apples, peaches, citrus fruits, cucumbers, tomatoes, and bell peppers. Wax coatings are used on fruits and vegetables to help prevent moisture loss, protect from bruising (during shipping and handling), and increase shelf life. Waxes are also said to help reduce greening in potatoes although not only do they not do so, but they actually increase potato decay by cutting down on gas exchange in and out of the potato.
When purchasing non-organic fruits and vegetables, you should ask your grocer about the kind of wax used even if you are going to peel the produce. Carnauba wax (from carnauba palm tree), beeswax, and shellac (from the lac beetle) are preferable to petroleum-based waxes, which contain solvent residues of wood rosins. Yet, it is not just the wax itself that may be of concern but the other compounds often added to it: ethyl alcohol or ethanol for consistency, milk casein (a protein linked to milk allergy) as "film formers," and soaps as flowing agents.
Unfortunately, at this point in time, the only way I know of to remove the wax from non-organic produce is to remove the skin, as washing will not remove the wax or any bacteria trapped beneath it. If you choose to do this, use a peeler that takes off only a thin layer of skin, as many healthy vitamins and minerals lie below the skin.
Nonsynthetic waxes, including carnauba wax and beeswax, are currently permitted for use on certified organic fruits and vegetables. The National Organics Standards Board has also petitioned for unbleached orange shellac on citrus fruits, but this petition is currently pending.
For more information on this topic, see: Everything I Need to Know About Organic Foods