Well, this is probably WAY too long, but here's my take on a good intro movie:
The screen is black. It fades into view of a huge city. Camera is raised, so you're looking down slightly at it, from moderate distance (The FOV is big enough to encompass the entire city)
Camera cuts to a 'birds-eye-view', almost like looking down from a helicopter, scrolling across streets and buildings. On the bottom left, green letters type up, accompanied by a small sound as every letter appears. It reads:
Mumbai
(Month) (Date)th 2084
XXXX Hours
The text stays for a couple seconds as the camera continues to float around, giving us an idea of the scale and diversity of the city. The letters them fade away.
The camera changes to a human-level view shopping district. People are everywhere. Again, letters come up. This time it says:
The most densely populated city in the world.
After a couple of seconds, that fades away too.
Camera cuts to a crowded, darkened control room. Again, words appear.
(Name) Radar Installation
Couple seconds, fade.
Camera switches to one of the seats with a radar console, y'know, with the round screen and the sweeping line. The operator is leaning so that his head is offscreen, you can here him and another guy talking in... uhm, Mumbain?
Camera cuts again, now the radar display fills the whole screen. This view stays on enough for the viewer to watch the sweeper do a couple complete rotations. Nothing appears on the screen. (You could add a couple of blips with little words labelling them as civilian flights, but for this, effect>realism, probably)
Cut to a view of the sky. Couple small clouds. Sun is centered in at the top of the screen. Lens flare aims at the bottom left of the screen. The camera moves slightly, and the flare moves from that side to the right. As it points directly at the camera, so that theres a big flashed, the ships appear. 6 small ones. they swoop down, just barely allowing for a good enough view to allow the viewer to see they're not man-made.
Cut back to the radar display. Couple sweeps, nothing.
Cut to the crowded street. One of the ships lands, as people scream. One stays, curious. The ramp lowers. You can't see inside. A bright flash, and a plasma ball rips out, killing the lone person. Fade to black.
About 5 seconds of blackness, then an abrupt flash view of the fighting, followed by an abrupt fade to black. This repeats several times, before it goes back to black. The words type up again:
Bonn, Germany
The words fade into the black. Abrupt flash, a SAM launcher firing at the UFOs, as men scream. Fade to black.
Bangkok, (uhm... wherever it is)
Abrupt flash to combat there, fade to black, then the same sort of thing for the last city.
Scene inside the UN, people arguing, then the head person declares war.
The final scene is told through the eyes of the player character. It starts with you entering an office (Yours). Several people are inside. One is a UN rep. He says
"Ah, commander. Good to see you found your office. I'd like you to meet some people" He motions to the side, where the remainder are standing. The rep introduces you to Dr. Connor, Cdr. Navarre, all the people from the mailclient letters. You then go ans sit down at you desk. The people all nod, etc, and begin to file out. You pick up a manila folder on your desk. It has a top secret stamp on it, and the word Phalanx along with the phalanx logo. The screen fades to black, and only the Phalanx and the logo remain. They stay for several seconds, then they fade too. The name of the game fades in, UFO: Alien Invasion. That fades out after about ten seconds. End of intro.
