A question of morality
If your answer is yes, then congratulations: you would be one of the "good" Forsaken, like Leonid Barthalomew, "the Revered," who view undeath as a kind of disease to be treated with the proper medicine, firm in the belief that there is a cure to be found somewhere out there. But you would no longer feel any pleasure in being good, no sense of moral satisfaction, or swell of righteous pride in your blood. You do what is right purely because of your firm conviction that it is the right thing to do.
If your answer was no, however, or perhaps a confused shade of "I don't know," then welcome to the massed ranks of those former humans who dwell in a state of moral ambiguity, sometimes unable to tell right from wrong, and sometimes unable to care.
In order to roleplay a Forsaken well, you must also understand the story of the humans of Azeroth, because the Forsaken were once human too. If you haven't read that story already, be sure to do so now. The Forsaken of today would have once been, for the most part, the soldiers, farmers, or other inhabitants of Lordaeron, caught by surprise when their entire grain supply was infected with the undead plague. Through no fault of their own, they were infected with the plague that twisted their bodies into mindless zombie slaves of the evil Lich King, soldiers in his unstoppable Scourge.
A twisted mortality
The people of Lordaeron's dead bodies were no longer under their own control. They were forced to witness first hand as their own arms and legs started to carry out the will of their evil master, perhaps even inflicting violence and death of people they once loved. Perhaps all this would have been too much for some, and fortunately some Forsaken may be blessed with no memory of this time.
The torture of this slavery did not last too long, however. Soon, the Lich King began to lose control over some of his zombies, enabling them to regain their own consciousness and identity. (Your character probably wouldn't know too much about the reasons for this, except that it might have something to do with an attack on the Scourge by Illidan). Sylvanas Windrunner, once Ranger-General of the high-elven city of Silvermoon, was among the first to regain control of her own mind, and it was she who rallied the others into one force, and defined for them their new identity as Forsaken.
Together, they fought a war with the demonic Dreadlords who sought to take advantage of the Lich King's weakness to kill Arthas and take Lordaeron for themselves. Sylvanas and the Forsaken were victorious, of course, and they set up their new home in the bowels of Lordaeron city, now known as the Undercity. Now, about 5 years have gone by since those fateful events, and the Forsaken are still fiercely loyal to their savior... for the most part.
Guess who's coming to dinner
It is known that Sylvanas is preparing some kind of new plague to be used against the Scourge forces in Northrend. Some say that this new plague should not only be used on their undead enemies but on the living as well. Still, the Dark Lady Sylvanas holds her secrets tightly, and the Royal Apothecary Society isn't telling much either.
Although Sylvanas has arranged for them to officially be part of the Horde now, there are many questions as to just how committed the Forsaken are to this new relationship. Many of the living simply cannot accept the undead, although there are some, especially among the tauren, who hope to help the Forsaken somehow undo their curse of undeath. Everyone is hesitant to associate with the Forsaken at first, but it is not impossible for them to form true relationships with people. Perhaps they could even become close enough that the Forsaken wouldn't have them over for supper... so to speak.
For more information about the Forsaken, check out WoWWiki's information, as well as the life-story of Sylvanas as the focal point of the Forsaken story. Dramatis Personae, as always, has an excellent quick start guide to creating a Forsaken character, too. Finally, there are many interesting things to come in the Forsaken story with Wrath of the Lich King, though you'll have to experience those for yourself.