If it's an e-ticket, I usually print the emailed receipt, and later when i'm at the airport I ask for a 'real' paper receipt on AA stock paper. If it's a paper ticket, the last page is a receipt. Before the flight you can also call customer service ask ask for a printed receipt. They will mail one to you.

If you already took the flights, AA will ask for a processing fee to "find" and "print" the receipt for you. Or you could use your credit card statement, as a previous poster suggested.