as do I - it's wonderful, and if you ever had electronics die after warranty ends (within 3 years) they have an amazing program to make you whole within minutes, no hassle, no costs... I would fight for my AmEx!
Funny enough, I get better customer service from Discover with their card then I get from Amex with my $500/year Platinum card. I've found my experience with Amex in general to have gone downhill over the last ~5 years or so.
I've personally lost my platinum card about 7 times and it is the most pain-free experience. Also I've had a number of fraudulent charges and amex just wipes them away. It's wonderful.
I received the exact same level of service from Discover over the last 2 years. Lose my card? They overnight it to me at no additional charge. Fraud charges? Never had an issue with a dispute.
I've found Amex's concierge to be okay and their travel product prices to be absurdly high. The only reason I keep my Platinum card is because I get $200 in Southwest gift cards each year with their airline reimbursement, and they reimburse me occasionally for my Global Entry membership renewal.