We've come for your daughter, Chuck
If WoW had a strict alignment system, the Undead would be the race closest to chaotic evil. It's true that they, like every other race, are interested in preserving their own survival, but they go a little bit farther than most, including the concoction of WoW's A-Bomb; a deadly plague the effects of which are shown here:
Somebody's been usin' Brand Xxxxxxxxx
The Undead (or Forsaken, as they call themselves) are the byproduct of a corrupted Prince Arthas' descent into villainy. One of the major figures as the game began, Arthas began his time in the spotlight as an Alliance hero, and a powerful paladin. When followers of the evil Lich King infested Stratholme, one of his kingdom's cities, with plagued grain, the citizens began to turn into the undead Scourge. Arthas defied the orders of his superiors and slaughtered every citizen in the city, which began the obsession to punish those responsible, and eventually cost him his sanity. He eventually became enslaved by the cursed sword, Frostmourne, and became a full-fledged villain. One of his first items of business was to storm the city of Silvermoon, home of the high elves, in an attempt to use their mystical Sunwell to revive a powerful Lich. On his way, he slaughtered numerous enemies, one of which was Sylvanas Windrunner, a ranger, who gave Arthas such a hard time that he chose to raise her from the dead as his slave after killing her.
Eventually, she and a large gathering of her followers, found a way to break free of Arthas, and became the self-titled Forsaken. When a player begins the Undead campaign, they have just been raised from the dead, and are immediately dispatched to fight a war on two fronts; one against the mindless Scourge, and another against the zealot Scarlet Crusade who seek to wipe out every undead in existence.