SPOILERS AHOY! I've avoided a lot of details here, but if you're trying to avoid hearing about what happens at the end of the Icecrown Citadel encounter, you might want to skip this post.
We were enslaved by the Lich King, turned into abominations against all we stood for and then used as fodder for the Scourge's battle against all we cared for in life. Freed by the power of the Light, we swore vengeance against him and his armies for what was done to us. It was our reason to carry on in unlife, giving us fuel for our unholy inner fire. We would destroy Arthas for what he did to us.
And now Arthas has fallen. So now what?
Those of us who are RPing as Death Knights have now, with the fall of the Lich King, found ourselves at the end of the story arc that started the moment our characters were rolled. The Knights of the Ebon Blade were formed with the sole purpose of taking down Arthas. What's next for our characters now that he's dead? Is there anything left to unlive for?
To begin, it's worth noting that the Scourge does still exist. Bolvar Fordragon's sacrifice is keeping them in check, and presumably they will no longer be spreading, but one goal for your character could be helping to clear out what's left of the Scourge. There may be even more potential here once we learn more of what will become of the Plaguelands and Ghostlands in Cataclysm. There are rumors of a possible Alliance push into the region, giving the Alliance more of a foothold against the Forsaken and Blood Elves. If the land is being retaken, either by Horde or by Alliance, your character could dedicate themself to aiding in that effort and retaking old Lordaeron. This is an especially good hook for human, Forsaken, or Blood Elf Death Knights, for whom retaking the old homeland can be a very personal cause. It will take a long time to reclaim the land from the plague, but clearing out the Scourge is a good start. Death Knights are especially suited to working in the Plaguelands as undeath would make them immune to many of the toxins lingering in those blighted lands.
But maybe now that your character's need for vengeance has been sated they would prefer to focus on their own people. With talk of increasing tension between the factions in Cataclysm, your character may dedicate themself to harnessing their unholy power in defense of their people and their homeland. For those who have fertile, vibrant homelands to return to, this can also be a deeply personal cause, but one that may remind them of just how much they have changed since death. They may find themselves more driven to defend it because of this, desiring to protect in others what they themselves have lost. Alternately, they may find themselves feeling alienated. A Death Knight feeling that they no longer belong in their own homeland may take up the mantle of anti-hero, protecting those who fear them out of a loyalty deeper than the living will ever understand. Or they may decide to find a new cause or a new people to defend. Horde Death Knights of any race may find themselves more comfortable with the Forsaken than their own people and may choose to take up their causes.
Or maybe your character has something even more personal to motivate them. Perhaps they still have living loved ones to protect. Perhaps they've found another purpose on the path to vengeance and they now choose to dedicate themselves wholeheartedly to it. Perhaps they have a friend or loved one with their own path to follow, and they choose to join them. For those Death Knights who have rekindled old connections or forged new ones, finding a reason to go on after the fall of the Lich King is a little easier. Even Thassarian has a little sister to return to.
Remember, though, that a peaceful retirement is rarely the fate of one who has been bound to a vampiric runeblade. The fact that the Death Knights still retained their power after being freed from the Scourge proves that the cursed weapons don't rely on Arthas' existence. What they do require, however, and what they will continue to require is souls. Whatever path your character takes, it will be guided at least to some degree by that need to satiate the runeblade's hunger. Fortunately, in the world of Warcraft, a noble cause to kill for is never hard to find.