It's no surprise that Al Qaeda and their like are successful againt nation-states. They are the very model of a spontaneously self-organizing phenomenon when it comes to asymmetrical warfare: small groups of individuals who do not necessarily take orders from a single central commander, other than a shared ideology and common goal (the destruction of the West).
(Let the rambling commence.)
Until just now, I thought it would be nearly impossible to eradicate their cancer from the world in less than 20 years; how do you fight a dispersed threat like this in anything other than an intergenerational fashion? However, I have recently realized that an emergent phenomenon must "emerge" within a context or environment; that environment can be beneficial or harmful to emergent behaviors. Change the environment, either by disruption or destruction, and the emergent behaviors must necessarily dissipate, deform, or die off -- perhaps in unexpected ways, but the behaviors cannot be expected to be the same after as they were before.
That's one way for a large centralized power to fight a dispersed threat: go after the enabling environmental factors that give rise to and support terrorist cells. On the international stage this means one thing: either a nation is with the terrorists, or it is with the U.S. fight against their evil. If a nation-state actively eradicates the cells that exist and reforms their policies to be unfriendly to emergent terrorism, that is the environmental disruption needed to be "with" the U.S.
Of course, another way to alter the environment is to destroy it -- c.f. Iraq in almost all areas except the Sunni triangle, and even that will be coming along soon. That destruction has a disruptive effect as well; you can't think that Iran and Syria are smiling -- they know we mean business, and must either be friends or foes. Look like Iran, at least, is going for "foe" status -- insh'Allah their people will rise against the mullahs to free themselves.
(Let rambling cease, for now.)