"What would be the purpose of a terrorist attack? Here are some guesses, and a look at what's happening.

1: Kill and maim Americans.
2: Cost America money.
3: Damage American prestige throughout the world.
4: Reduce American influence throughout the world.

I mean, if you were a terrorist that would be a pretty ambitious agenda. Not one you could hope to achieve by yourself."

These are some pretty silly reasons. The terrorists have killed and are killing far more Muslims who aren't American then Americans. Now, maybe they trying to kill themselves while fighting Americans, at least this makes sense. They could think they could go to heaven if they are trying to do this. Obviously to their mind Americans are vastly more significant than themselves. Another aspect is the American soldier is a honorable and brave warrior, so to a primitive mind it's better to try to kill a lion, rather than die trying to kill a squirrel.
So change 1 to
1: trying to die fighting a superior foe, so as result they go to Heaven.

Therefore it seems they have achieved this to some extent- many have killed themselves, but it seems that the ones still living, apparently having some doubts about this route to Heaven and in general have got somewhat sidetracked from this possible goal as the war has progressed.

As for:
"2: Cost America money.
3: Damage American prestige throughout the world.
4: Reduce American influence throughout the world."

They may be trying to cost American money and damage American prestige in the world, in order to reduce Americans influence throughout the world. And they doing this because they want to control one country and expand this to control many countries.
And this probably is failing, because they seem to have lost The Base, and Americans and the rest of the world are hunting them down. Whereas before 911 they were definitely making some progress in this area.

I think American prestige has risen in the world, because more people of the world have realized that American's global security is something needed by them rather something the American are doing because lack better things to do or because of some "selfish reasons". This is quite dramatically seen in Iraq, where most of the population *want* the occupational forces to remain in Iraq until such time as the Iraqi people can deal with their own security. And from an America prospective we not only want Iraqis to be able to handle their own security but we eventually want Iraqis get to the point of being able to project security beyond their borders, so as to increase regional security.
Prestige is a very important aspect of this war against Terrorism. Prestige should not be confused with being liked or loved. Prestige has more to do with being able to trusted, and dependable. You get a lot of prestige by doing the seemingly impossible- going to the Moon with the Apollo program for example. You can also get prestige in simpler ways like building big buildings or bridges. The reason [the only vaguely rational POSSIBLE reason] for Iran wanting to make a nuclear bomb is for prestige.
Of course the only vaguely possible reason for 911 was for the terrorist networks to gain prestige.

The amount of prestige that Iraqis can gain by becoming an independent and free nation is HUGE. That Iraqis braved the bullets and voted despite the threat was something the world thought as being very noble. The Iraqi soldier fighting and dying for their country is perhaps not as recognized at the moment by majority American people, but I think the Iraqi people are quite aware it's importance, and everyone in the world will in coming years become undoubtedly more aware this.

Looking at the sweep of time of last few centuries, America has won, and it's good bet America will continue to win. The terrorists have never won [in all of history] , and they will probably continue to lose. But if they actually do the impossible they would gain enormous prestige- though this not mean they would able to transform this prestige into anything other then vast piles of human bones with massive increase in disease and suffering. The only "good" connected to what the terrorist are doing is they make it very clear to the less wise there is actually a thing called evil.