Many of the world's islands have indigenous populations that have occupied them for hundreds or thousands of years before the arrival of Europeans and other seafaring cultures, which spread across the world in the period roughly between 1400 and 1800, depending on location.
Islands with indigenous populations include Madagascar, which is off the southwest coast of Africa; New Zealand, to the southwest of Australia; the Hawaiian Islands, located in the center of the Pacific Ocean, and almost a thousand miles away from other island systems; the Canary Islands, off the eastern coast of Africa; Easter Island, one of the most isolated islands in the Pacific Ocean, and many others. Most were colonized between 1500 BCE and 500 CE, with some of the latest (such as New Zealand) being colonized around 800-1000 CE. Indigenous people arrived using simple canoes and a variety of navigational tricks, including reading the stars and following the flight patterns of birds. Since some islands are very isolated from one another, they frequently develop distinct cultures, languages, and customs. Many of these have been lost due to dilution with global cultures.
However, not every island possesses an indigenous population. Some were missed for whatever reason, such as being too remote, intimidating terrain, a lack of plants and animals, or being too close to the poles. Some of these islands are so remote that prior to artificial introduction, they lacked mammals and/or reptiles, and only possess plants, invertebrates such as insects, and birds. These remote islands may not have been inhabited by any animal larger than a seabird since their creation millions of years ago.
There are many islands that lack indigenous populations, and their histories are interesting because they are generally completely known, as serve as microcosms of human behavior in small areas with limited resources. Examples in the Indian Ocean include the Seychelles, just north of Madagascar, that wasn't sighted until 1502; numerous islands in the southern Indian Ocean, which are part of the French Southern Territories, including the Crozet Islands, Kerguelen Islands, Île Amsterdam, and Île Saint-Paul; and the Cocos Islands, southeast of Indonesia, currently a territory of Australia. Some of these islands, especially the southernmost, lack trees entirely or are constantly cold and windswept due to the Antarctic Circumpolar Current.
There are a handful of islands in the central Atlantic Ocean, caused by cooled magma released from seafloor spreading on the mid-Atlantic Ridge, which were uninhabited until their discovery by European sailors. This includes the Azores, about a thousand miles west of Portugal, which appeared on maps from the 13th century but was not colonized until 1427; Saint Helena and Ascension island, equidistant between Africa and South America, which are among the most isolated in the world, and were used as staging areas for the Allies in WWII; and the familiar Iceland and Greenland in the north, which were reached by Scandinavian sailors sometime around the year 1000.
Many of the other islands without indigenous populations are near those previously stated, or in the far north where it's too cold for trees to grow. Of course, Antarctica is a continent without an indigenous population, being far too cold. Most of the islands of the Pacific were colonized long ago, due to their abundance and a mild climate.