My favorite explanation of Basque's origins comes from my Basque friend who claims that Basques came from Atlantis. :-)
I'm in the process of adding Basque to my list of languages (joining English, Spanish, French, and smatterings of German and Swedish) though at this point I find Basque so complicated that it's hard to imagine getting much beyond the level of basic phrases!
I have my own, less flattering pet theory: They are the descendants of Neanderthals, who perished on the Iberian peninsula some 30 000 years ago... ;-) The world's northernmost desert wind.
Aye... Southeastern Europe has a lot of these (and the fools who believe it are often rabid chauvinist politicians, so it is less funny).
For example, in Hungary there is 'theory' that Sumerians were Hungarians... *Traitor*, n. A benighted individual who perceives an illusory distinction between serving his nation and abetting the criminals who govern it.