With Death Knights getting their own starting zone and their own heroic storyline, it was often wondered whether they'd share the same opening cinematic as their individual races. We have the answer now: They do get their own unique cinematic, shown above.
There's two major things I took away from the cinematic. First, it gives a solid origin story for Death Knights: You were apparently slain in combat with the Scourge, but raised to become a Death Knight. So the ideal of the PC Death Knight seems to be a hero who was made an unwilling victim, which makes the fact that he or she is welcomed back by the Horde or Alliance possibly much more believable. As you awaken as a fresh level 55, you are also apparently still under the thrall of the Lich King, which should make for an epic newbie zone experience as you struggle to regain your freedom.
Secondly, the opening cinematic has a wonderfully ominous picture of Acherus, the Ebon Hold, home of the Death Knights, looming above Light's Hope Chapel -- a perfect setup for the coming war with the Scourge, that drives home how immediate the threat is.
Oh, and do be cautious, this cinematic has a high chance of getting you way too fired up to play a Death Knight.