It really depends on the mechanics of the game. When you create your character in FFXI, you're still you but you have a graphical representation of you in the game. You wouldn't want 2,000 identical characters running around saying that they're all different people. On the other hand, playing as a character with a seriously deep background is far better when playing a game for the story, in my opinion.

It just depends on the game being based on story or interactivity, I guess.