Very small islands--say, islands smaller than necessary for any useful purpose, but still larger than rocks--are called islets.
There are three general types of islands: continental, river, and volcanic.
Continental islands are islands that are connected by the continental shelf[?] to a continent. Examples include Greenland and Sable Island in North America, Barbados and Trinidad in South America, Sicily in Europe, Sumatra, Yap and Java in Asia, and Tasmania in Australia.
A special type of continental island is the microcontinental. which is caused when a continent is rifted[?]. The best example is Madagascar. The Kerugelen Islands[?] and some of the Seychelles are other examples.
Another subtype is the barrier island, which are accumulations of sand on the continental shelf.
River islands occur in river deltas and in large rivers. They are caused by an accumulation od sediment when the carrying capacity of the river is lowered.
Volcanic islands are caused by volcanoes. Because they are not connected to continents they are not geologically part of a continent.
One type of volcanic island is that of the volcanic island arc. They are caused by the subduction of one plate under another. Examples include the Marianas Islands[?], the Aleutian Islands, and most of Tonga in the Pacific Ocean. Only some of the Lesser Antilles and the South Sandwich Islands are the only Atlantic examples.
The last type of volcanic island are those formed by hot spots. The hot spot is stationary relative to the plate above it, so it leaves a chain of islands in its wake. Those islands are eventually eroded down and become seamounts. This is why there are parallel lines of islands in the Pacific Ocean. The northernmost chain is the Hawaiian Islands, from Hawaii to Kure[?], and then turns north as the Emperor Seamounts. The next chain is the Tuamotu Archipelago[?]; its bend becomes the Line Islands. The southernmost chain is the Austral Islands[?], with its northern branch as most of the atolls in the nation of Tuvalu. Tristan da Cunha is an example from the Atlantic Ocean.
A special type of the hot spot island is the atoll; it is formed when a coral reef builds up around a volcano is it is eroded beneath the waves, resulting in a ring-shaped archipelago of islets around a lagoon. Obviously, atolls only occur in the tropics. Eventually even atolls will be eroded away, leaving an awash reef like Kingman and then a seamount. Palmyra, Wake, Kwajalein, Chuuk, Midway and the entirely of the Marshall Islands are atolls. There are no atlantic atolls.
See List of islands for a listing.