Warning: the video above contains spoilers, of sorts! Really, it's the same thing you'd see almost immediately upon powering up The World Ends With You, but you may not want to see story sequences until they're coming out of your DS screen -- even if we've discussed the premise before.
This cutscene is the opening to the game's first day, and introduces the protagonist Neku Sakuraba and his bizarre predicament. Because it's a Square Enix game, the opening cutscene is twelve minutes long. That's not really a complaint, either. People buy the company's games for the storytelling -- actually interesting gameplay like this is kind of a bonus! Check after the break for the second and third days' story sequences (which may contain for-real spoilers).