American Airlines website specifically says that you can carry a guitar as cabin baggage as long as it can be "stowed in the overhead space". However, hostesses do stow them away safely but not in the overhead bins. At customs, you can declare the guitar (if it's bought sometime before) as for personal use and not new. I did not face any issue when I brought my Gibson from the states.
Keep in mind that you might not be able to carry any further cabin baggage. It's best to call the airlines and confirm.
My gear, currently up for sale
Washburn X-16 anarchy - SOLD!!
duncan pickups - I wonder why Im selling these.