I have a Amex Platinum and have been very disappointed with their concierge program. I've used the service twice, both times using their online/e-mail system (I've never called in)
1st try: Was going to Chicago, for a weekend, on vacation. I wanted to catch a Cubs game at Wrigley Field while I was there. The games were sold out, so I put in my request. I asked for two tickets, up to $100 each, best seats available. It took at least 3 to 4 e-mails back and forth before they figured out what I wanted. Each time a different concierge reply to my request. When I finally got a response, the tickets where in the upper, upper level, and were over $100 each. I ended up using a ticket broker online and got tickets right behind home plate for the price I was looking for. Very disappointing.
2nd try: Was looking for a Wii Fit, which was sold out at all the stores I checked. I received a response in less than 48 hours. However, the Wii Fit they were able to find was marked up over $100, not including shipping. Even the listings on Craigslist and Ebay were less!
All in all, I haven't been very impressed with Amex's concierge program. There isn't a fee for the service, persay, but for a $450 annual fee, I expect more. Hopefully others have had better luck!