If I wanted to annoy the entire world and (possibly) end some lives, I'd put up anywhere from a 3-24 hour long Nyan Cat loop.
Otherwise, I think I'd pick something off of OverClocked, preferably something soft and melodic to ease the tension of the world. Some options would be Pearl Song - SM64 [http://ocremix.org/remix/OCR00952/], Home Again - Earthbound [http://ocremix.org/remix/OCR01545/], Escape into the Twilight - NiGHTS [http://ocremix.org/remix/OCR01734/], or Pachelbel's Ganon - OoT [http://ocremix.org/remix/OCR00753/], just to name a few.