"In the year 591 A.D. the Byzantine King Mauricius was contesting the Roman Empire in Thrace. Here he captured three Slavs. To the astonishment of Mauricius, he found these Slavs unarmed, carrying with them only a tambura. With surprise he asked these Slavs who they were and what was that in their hands? They replied, 'We are Slavs and we live along the Western Seas (Adriatic). We play tambura because in our country there is no iron and we live in peace. We do not know the meaning of war bugles.'" from History of the Tambura, Walter Kolar
I first heard tamboura in recordings of eastern European gypsies and field recordings of Yugoslavian village music. It's got a lovely sound, somewhat exotic to American ears, and is in truth the name of an entire class of instruments popular in Macedonia, Bulgaria, and other parts of eastern Europe. The tamboura is looked upon as the national instrument of the Croatians (now that they're no longer supposed to be part of some nation called "Yugoslavia"), where it is the basis of a style of music called tamburitza.
The Slavs apprehended by Mauricius most likely used their tamboura as a solo instrument. It would accompany singing or dances. But where did it come from, before it came to the peaceful "Western Seas"? Some sources say the tamboura was brought to Croatia by the Turks, and that it came from Persia (what we now know as Iran).
There is a long-necked fretless lute, known as tambura in the south of India and tanpura in the north, which is crucial to raga music. It usually has four to six strings which are plucked lightly and continuously; the tamboura player would sit behind the lead musician so their drone could be contantly heard. That drone, subtly nuanced and constantly there, has been characterized as the fabric upon which the tapestry of the raga is embroidered.
Although the drone has long been a part of Indian music of both the northern and southern styles, there is "no evidence that there were any long necked type instruments before the Muslim invasion of India." (http://www.psychokey.com/sitar/sitarhistory.htm) This family of instruments seem to have been spread by Muslim influences (the Turk and Afghan rulers of India, for example) after its development in Mesopotamia. There are references to tamboura in Greece as an example of Byzantine influence; the Byzantine Empire can also be seen as a meme spread vector in this case. This multifarious lute mutated into many forms over time and with exposure to many local cultures, including the Russian balalaika, the Italian mandolin, Turkish Saz, North African nefer, Indian sitar. The tamboura itself is found in different shapes, even in the same region. The Croatian bisernica, or "little pearl", is tiny and used as a high voice in tambourica bands. The šargija has a small oval body and more commonly used as a solo instrument than as part of the tambourica bands. And the bugarija looks, well, like a guitar; it's much larger and used as a rhythm instrument. Indian tambouras, on the other hand, have long necks and deep but short bodies. They are played upright, with the musician sitting on the ground. These are all considered part of the same family!
The tamboura has been spread by many influences, including migrations, battles (the changing fortunes of empires), and wanderers. With the growing popularity of (cover your ears, i'm about to say it) post-modern mixty-matchy music that pulls from influences all over the globe, this sound is becoming less exotic to American ears. It's the spread of empires, moved forward to the twenty-first century.
(Thank you shallot)
Other useful sources:
http://www.larkinam.com/MenComNet/Business/Retail/Larknet/ArtTamburitzas
http://home.pages.at/tamb/english/instruments.htm
http://www.psychokey.com/sitar/sitarhistory.htm
http://www.geocities.com/hellenicmind/byzantium.html