No they haven't won. The terrorists will never bring about the downfall of the Western World as they claim thats what there out to do. They don't have the resources, technology, or manpower. Thats why they lose battle after battle and always have to resort to suicide and roadside bombs.
But as others have said it is impossible to stop terrorists as they will always exist just the same way there will always be crinimals. Murderers, robbers, rapists. They'll always exist. You can defeat Al Queda and conquer Iraq. But can't ever wipe the world clean of terrorists.
The key here is awareness. The United States needs to know they exist and know how to stop them. Not set out on this ridiculous and impossible quest of purging the world of terrorists. Which a lot of people claim is just a front as a way to claim oil.
What the US should have done is kept on it's original goal in Afghanistan and fully defeated Al Queda and the Taliban eliminating Osama and throwing them out of power. You can kill all of them but you can crush an organization like Al Queda. Had they stuck to this original goal Al Queda would be defeated by now and Bush and the US would have been much better off in the public eyes of the world and the world would be a little bit safer of a place. But instead Bush left the job half done and went on his way to Iraq. Inspiring more hatred than needed and causing more problems than solving.