Vidalia Onion

This onion is one of the most popular types of onions out there with a sweet taste. The Vidalia onion was orginially grown in Georgia and named after a city that hosted a large farmer's market. Vidalia onions are usually used in onion rings and the fried "blooming onions."

Italian Red Onion

Italian red onions can either be sweet like the Vidalia or mildly spicy. These onions are often used in salads as rings or diced cubes.

Yellow Onion

Yellow onions are not very tasty but they are used in most recipes. However, where the yellow onion lacks in flavor, it does make up in price. In other words, the yellow onion is not expensive.

White Onion

White onions are small with a mild flavor. They are often used in beef stews and other meat dishes, and due to their mild taste, they are usually served whole or cooked in a sauce.

Green Onions

(Also known as scallions) The green leaves is the part of the green onion that is eaten. Because of the bright green leaves, the green onion is usually used as a decoration in soups, salads, and vegetable dishes.

References
http://www.bellaonline.com/articles/art16445.asp