My candidates:
Final Fantasy X: Kind of narm, but still well put together. It's kind of weird how it goes through about halfway before you get to the title screen, and then goes through once you start the game. W/e
Shenmue: FATHER! NOOOOOOO! Jokes aside, this is probably the most cinematic intro I've seen yet. And in the actually good way, not 30fps garbage.
Fallout: Easily the best, by a faaaaaar margin. Excellent music, excellent visuals (I'm a sucker for late 90s pre-rendered 3D), and manages to be short and to-the-point while also giving you plenty of information about the world and its circumstances. Must see: