I've never understood why anyone would want the standard, high-annual-fee Amex personal card. Most of the no-fee Visa and MC cards have virtually unlimited charge limits, cash-back or other rewards programs, and convenient year-end accounting statements. Plus, many of the places we go don't accept Amex cards because of the relatively high fees Amex charges merchants. I have a number of friends that have the Delta Airlines Amex card for the FF points, but, given the difficulty of using points and the implicit exchange rate, I'd rather have cold, hard cash back. Many years ago, there used to be some comfort in carrying an Amex card when traveling abroad, but that hasn't been an important issue for about 20 years.
Because Amex offers services that other card companies don't. For instance, I travel a lot, and my Amex doubles as a membership card to every major airline lounge; I have a quiet place to work and relax at the airport. There are a number of other travel benefits, like guaranteed hotel and car reservations, free hotel and car upgrades, etc. It also has its own AAA-type program for my personal car.
Another nice perk--if you like to eat--is that Amex holds tables at some of the nicer restaurants around so I can often get a reservation through Amex when I can't through the restaurant; same for tickets to concerts or sporting events.
There are also some nice shopping perks, like doubling the warranty on my purchases, allowing for returns if I break or lose something I buy, etc.
I was in New York on vacation some years ago, and I went to the US Open. I was leaving that day, and the tennis center happens to be not far from the airport, so I brought my bags with me to the tournament. I didn't want to lug my bags around all day, so I called AmEx. "No problem," they replied. "Come to the AmEx booth when you get in and we'll hold your bags for you. I'll call ahead and tell them that you're coming." Now that's service.
There are probably other cards that offer similar perks, but I've not seen one that offers everything that Amex does at a similar price.