Those new kinds of perforated produce bags work because they allow the produce to get some air. Potatoes, grapes, cabbage, citrus, carrots and apples have low respiration rates, so they keep well. Lettuce and green beans breathe much faster. Keeping produce cold and limiting its oxygen is the key, but not everything wants to be stored the same way. Once injured, they rot instead of ripen.
Tomatoes deserve special mention.
Corriher points out that one of the critical flavor components of tomatoes disappears when they are chilled. Keep them at room temperature. Tomatoes are fruits, remember. Wrapping fruits and vegetables in plastic limits their oxygen supply and thus keeps them fresher longer. Keeping them moist helps, too.