If you prefer to keep the mystery about a game before you play it, watching the video below would be a terrible idea. Otherwise -- weeee!
The footage in question covers the first five minutes of story-driven action game BioShock Infinite. Assuming you've played the original and fantastic BioShock, you'll notice many subtle similarities between these first five minutes and the first five or so minutes of that one -- I've included both videos for reference (and let's face it, any excuse to watch that intro again is a good one).
First few minutes - YouTube