Jerome,
Tripods are allowed as carry-on when flying within the United States, and for international travel to and from most countries. Your tripod may be counted as a 'carry-on' item should it cause your bag to exceed the maximum carry-on size allowances set forth by your airline.
Tripods must conform to airline specified carry-on requirements. It is best to remove the head and pack that in your carry on, bringing only the legs through security separately. Having spoken with dozens of photographers about this topic over the last three years, for some reason tripods with the head attached cause more problems from misinformed TSA screeners than those with the head removed.
I fly with my tripod on the exterior of my bag depending on the job, and fly with one or two Manfrotto 3373 compact light stands attached to the exterior of my backpack of a consistent basis. In one trip earlier this year in the span of 3.5 days I passed through security in Providence, Philadelphia, Frankfurt, Hong Kong, Incheon, Tokyo and Chicago with a Manfrotto 3373 light stand attached to a North Face Surge backpack and no one blinked twice at any security check point at the airport (they did remove and inspect my Pocket Wizards in Incheon and Chicago though (at least I think those were the two airports that checked them out).
I address the subject of flying with a tripod exterior to my bag at www.flyingwithfish.com
if you search "tripod" or "Manfrotto 3373"
Happy Flying