I've only ever had one problem with Amazon, and it wasn't really them.
I ordered an mp3 player from another company through Amazon, and selected 2 day shipping because I wanted it quickly. This particular store only used DHL for shipping.
It went out the same day I ordered it, with an estimated delivery date of two days later. On that date, the tracking site said it was out for delivery. When I came home from work, no mp3 player. I checked the tracking thing again, it said "lazy delivery guy is lazy" and it was back at the office place.
Three days later, it hadn't moved. So I called DHL and asked "what the fuck?" and they pretty much said they'll deliver it when they felt like it. Then I asked if I could just come pick it up and they were like "No, GTFO" and hung up. I finally got my thing like a week later, as which point I sent a complaint letter to DHL (no response) and an e-mail to the seller recommending they not use DHL anymore (received a "thank you for your suggestion" e-mail back.) I don't understand the lack of response from DHL. At the very least businesses will reply with an apology form letter, and most of the time they'll give you something. Seriously, write to McDonalds or something with the most frivilous complaint you can think of (my cheeseburger only had TWO PICKLES on it instead of three! I'm OUTRAGED!) and at the least you'll get an apology and some coupons. Hmm... maybe DHL just hasn't had the time to respond yet. I mean, it was only a year and a half ago...
Anyway, Amazon is good, but DHL sucks.