The cuisine of the Native Americans was of course the first American cooking style, and it lent a great deal not only to subsequent American cooking but also to culinary styles around the world. Turkey, corn (maize), beans, sunflowers, potatoes, peppers, and various forms of squash (including pumpkins) are among the Native American foods now widely consumed elsewhere. Superimposed on this original native diet is the massive contribution of the various immigrant groups; many dishes considered quintessentially American are in fact based upon the cooking traditions of other countries. For example, apple pies, pizza, runzas, chowder, and hamburgers are all either identical to, or derived from, European dishes. Burritos and tacos similarly have their origins in Mexico. Information from Wikipedia.com
One characteristic of American cooking is the fusion of multiple ethnic or regional approaches into completely new cooking styles. The cuisine of the South, for example, has been heavily influenced by immigrants from Africa, France, and Mexico, among others. Asian cooking has played a particularly large role in American fusion cuisine.
Similarly, while some dishes considered typically American many have their origins in other countries, American cooks and chefs have substantially altered them over the years, to the degree that the dish as now enjoyed the world over may even be considered American. Hot dogs and hamburgers are both based on traditional German dishes, brought over to America by German immigrants to the United States, but in their modern popular form they can be reasonably considered American dishes.
Many companies in the American food industry develop new products requiring minimal preparation, such as frozen entrees. Some corporate kitchens (e.g. General Mills, Campbell's, Kraft Foods) develop consumer recipes featuring their company's products. Many of these recipes have become very popular. For example, the General Mills Betty Crocker's Cookbook, first published in 1950 and currently in its 10th edition, is commonly found in American homes.
American cooking has been widely exported beyond its borders. Fast-food burger bars, pizzerias, Tex-Mex, Creole, and barbecue restaurants can be found in cities all around the world.