The idea of a borderless, nationless world has been floating around in the back of my mind ever since I devoured all eight (at the time) novels in Orson Scott Card's Ender Saga as a twelve-year-old. If you never made it past Ender's Game (or if you've only seen the movie)—I promise it gets much better. Suffice it to say that in the aftermath of humanity's triumph over an alien species, Ender's brother Peter succeeds in unifying all the world's nations into a global hegemony, following which humans proceed to colonize the galaxy, develop a (surprisingly benevolent) super-intelligent being, and all is unicorns and rainbows.
While Card's vision of a unified Earth is perhaps a little too sparkly, I do think that there's a strong case to be made for a world without borders or nations, governed by a single, sovereign entity. I argue here that such a world would be, at the very least, more equal, more peaceful, and more productive. But, as always, feel free to yell at me and disagree.