Bungie put out a new Destiny trailer for E3 2014 that lays out the game's premise in a pretty straightforward way and also shows off a bit of gameplay.

UPDATE: The audio in this version is messed up. A replacement is uploading, and when it's done, I'll replace the embedded version here with the new one.

UPDATE 2: This version should have the fixed commentary audio.

A good mix of both gameplay and some additional story in Bungie's "New Beginnings" trailer for E3 2014.

Also the first time I think I've seen it explicitly stated (by Peter Dinklage's voiceover here) what I've suspected for awhile here-- that the Traveler was the cause of both humanity's lost golden age and its downfall, and the enemies we face are the enemies of the Traveler, not necessarily the enemies of humanity.

Still, that might not ever become relevant, but it is something I've been thinking about for awhile.