As was said by Crothian:
9/11 affected a lot of people in different ways.
And as was said by Henry:
It all comes down to really knowing your players.
Both of these statements accurately illustrate my beliefs regarding 9/11. However, it also comes down to what role you'd like 9/11 to play in your game. If utter realism is the goal of the game, right down to using accurate names, places, and history, 9/11 would be essential at least as a background story.
If, on the other hand, the game does not rely so heavily on realism - 9/11's placement in a game rests more on your players.
Put yourself in your players shoes with 9/11 events either happening or have happened. You are forced to make difficult emotional decisions based on your character's background, alignment, and loads of other mitigating factors. Some players feed off this kind of opportunity, others shy away from it, still others would loathe to be placed in such a difficult position.
Then you have the added problem of playing a superhero or Spycraft game with 9/11
about to happen. Can the characters stop it? Or are the events predetermined? These are difficult choices to make as a GM, and difficult to deal with as a player - at least from my perspective. Is all of that really worthwhile?
Again - refer to Crothian and Henry