oh alright then...
It would appear that there are a wide range of conspiracies - all with varying degrees of (im)plausibility.
At one end of the spectrum you have the 'controlled demolition' of the twin towers with super-mega thermite - all installed throughout both buildings in the space of a couple of exercise fire drills / or during a lift upgrade many years before (presumably on the off chance that it might come in handy)
-- One thing to bear in mind if you are planning to deliberately bring a large 101 story building down without damaging surrounding infrastructure and financial institutions - you probably don't want to fly a big **** off plane into the building first, that type of thing can really screw up your sums. You be better off picking a different cover story (McVeigh Mk II, or similar) -- And no, little Timmy wasn't told to do it by the man either.
Another reach is the deliberate act of flying the planes into their targets by agents of the US Government, this has been advanced in various forms from substituting the aircraft at the last minute, through providing a trained crew to buying a crew via ISI to do the job.
-- I had to giggle at the revelations of the head of ISI wiring Atta $100k on the 10th Sept. What the f#ck was he planning to spend it on? Maybe he just wanted to make sure his bills would be paid after he'd gone - it'd be a bummer to be blacklisted by his hotel. The paper trail in any of the above would be far too much of a risk for an organisation to proactively set out to orchestrate this attack, there are far easier ways to make a point.
Slightly more plausible (and this is relatively speaking mind you) is the idea that the Intelligence was available that the attack would take place and it was decided that the losses would be acceptable for the benefits they brought (bear with me and don't go off on one, purely a hypothetical exercise).
It is an accepted fact that a wargame was proposed (and declined by the Pentagon as too unrealistic) to 'run' the attack using a hijacked aircraft against the Pentagon building. Modelling exercises on potential losses in such a scenario had also taken place in the run up to the attack.
It is also a fact that aircraft that would usually be tasked to intercept straying passenger aircraft had been diverted that day to play with Migs and go on training exercises. I still find it difficult to believe however, that there were no aircraft available on task to run interference on an attack on the Capitol (this is day job, and the fundamental reason you have a widely dispersed Air Force, to provide Civil Defence).
Of course, nobody expected the Towers to fall. As conspiracy nuts (sorry, theorists) the world over would delight in telling you, it's unthinkable. There are many buildings that have survived aircraft impacts, there are also many buildings that have survived larger fires... someone clearly got their model wrong.
IF this was a deliberate failure to act, it was in anticipation of a couple of hundred casualties (less than have been suffered in the Mid East by service personnel since) not the thousands that occured due to the double collapse and certainly not the cruel twist of fate that led to the deaths of so many first responders and emergency service personnel.
The cost/benefit analysis would have to have been phenomenal to outweigh both the risk of getting caught and the moral objections involved in letting innocent people be killed (which is the way it would be couched - we certainly wouldn't kill innocent American's - we just might not stop them from being killed any more than we would patrol the nations highways 24/7 to stop people getting killed there - 42,196 in 2001, since you ask).
Sometimes, I think we all watch too much 24.
It is just about possible that the open goal the pilots had on the 9th September was down to negligence and incompetence, rather than a wilfull failure to act. Bearing in mind there would be an awful lot of people in both the military and civil aviation fields who's professionalism and better nature would put your carefully planned inertia at considerable risk, is it not more likely that this was just really crappy bad luck?
A bad thing done by bad people for bad reasons.