Eons ago, there were many places in Europe (particularly in France) where American Express was the only credit card accepted. And travelers could actually have their mail sent to American express offices in various cities, and they'd hold it for your arrival.
But that was, umm ...35 years ago. I don't know that there's anything particularly distinctive about American Express anymore.
It was also used to IMPRESS anyone you were with who instantly knew you were very important to have an American Express because they didn't just give those bad boys out to anyone. Of course nobody knew when you had to take a cash advance on a regular credit card to pay the balance of the American Express off each month.