Would American Airlines reprint my ticket?

You don't need a physical ticket these days. All you need is your Booking Code which you can find on your e-ticket that was sent to your email. If you don't have that, you can contact the airlines and they should able to give it to you once they verify that it's you. If they can't give it to you over the phone for security reasons, the check-in area have a list of all travelers, so, for local flights, you can get your boarding pass by just showing them your ID. Have a safe trip!

Why don't you reprint it yourself??? Last time I travelled I don't recall using a printed ticket at all. I just checked in and got my boarding pass.

You never had a ticket, hence you didn't lose it and don't need to reprint it.

American Airlines has been all electronic ticketing for years (like most airlines.) in

why not download the American airlines mobile app onto your phone, then you can pull it up and you will have your boarding pass.

Yes, you will just need your ID and the charge card you used to pay for the ticket. That will allow you to print the boarding passes at the ticket counter the day of the return flight.