Few plants actually self pollinate. The mechanism is seen most often in some legumes such as peanuts. In another legume, Soybeans, the flowers open and remain receptive to insect cross pollination during the day; if this is not accomplished, the flowers self pollinate as they are closing.
Self pollination, or more generally self pollenizing, limits the variety of progeny and may depress plant vigor. However, self pollenizing can be advantageous, allowing plants to spread beyond the range of suitable pollinators or produce offspring in areas where pollinator populations have been greatly reduced or are naturally variable.