While I believe there is probably a fair amount of brainwashing involved, I think understanding and education are going to go a hell of a lot farther than bombs in combating extremism. America's foreign policy needs to be re-thought if we want to stop leaders like bin Laden from ever being created; specifically the way we pump money into the Middle East. Instead of fueling Afghanistan's war against the USSR or giving Israel $13 million a day in foreign aid, we might want to fuel more constructive efforts like Greg Mortenson's, as detailed in Three Cups of Tea.
This is a complicated issue, and I don't pretend to have all or any of the answers, but as far as I can tell, understanding and acceptance are the keys to peace, not invasions and manhunts. It's been said before, and it will be said again, but although we have finally succeeded in killing bin Laden, our invasions and efforts since 9/11 have inspired a hundred more bin Ladens. I can't overemphasize the scope of the discordance between the US and the Middle East. I'm afraid (and I hope I'm wrong) that the death of one man will have accomplished little in the name of peace.