I've found a very interesting BBC article from the afternoon of 9/11 called Could the planes have been stopped? that talks about what the FAA and NORAD normally should have done. Here's a telling excerpt:

Air traffic control personnel "would have known immediately" when the planes veered away from their normal route, according to Mr Yates.

"They are monitoring the flight paths all the time, constantly monitoring them on screens in front of them.

"The controller would see straightaway that the flight profiles had gone away from the norm."

However, Mr Yates said there is little that can be done if a pilot is determined on destruction.

"Their first role is to get all other planes out of the way first - to warn any other contactable plane of close proximity and the potential for an accident.

"They will have been frantically trying to contact the planes that have gone off their trajectory.

"But if that doesn't work their only option would be possibly to scramble military jets."

Military planes can go into action "within minutes" in the case of an emergency, he said.

But if the plane changed course only shortly before reaching its target, it would have been too late.