I'm always hearing about how the British colonists "stole" the land from the Native Americans that were already living here. Are there any countries in operation today that are still being run by the indigenous peoples that founded it? By this, I mean the people who originally found an uninhabited piece of land, settled it, (possibly) formed a government, was never conquered by an outside nation (or managed to retake their land if it had been), and has never expanded their borders by means of invading another territory?
Iceland meets all of your criteria pretty nicely, let's go through them one by one.
Settlement. There is some evidence that the island was used by Irish monks on a seasonal basis before settlement by Norse/Gaelic people in the 9th century AD, but there were no indigenous peoples or large permanent settlements before that time. There is also evidence to suggest that the monks had left Iceland before the settlers arrived.
Government. The Althing (lit. all-parliament) was established in 930, and is arguably the oldest still-existing parliament in the world (although there was a 45 year period in the 19th century where it did not convene, so your mileage may vary).
Conquest. In 1262, after a lengthy civil war period (Sturlungaƶld), Iceland entered a union with Norway, which via the Kalmar Union became a union with Denmark. However, Icelandic chieftains entered this union voluntarily (there was no invasion, and the terms were very beneficial towards Iceland), and it lasted for almost 700 years, when Iceland became an independent republic in 1944, after being an independent kingdom in personal union with Denmark since 1918.
Border Expansion. The only incident that could be called an invasion by Iceland would be the Cod Wars. However, these are more properly described as a series of fishing boundary disputes between Iceland and the United Kingdom, with Iceland being the clear underdog. There were no casualties, and the result was an expansion of the Icelandic exclusive fishery zone, rather than acquiring any land.