I have bought games from Amazon (first class) and so far not a single one has come on the release date, or the next few days after it. GAME and Play.com are good for sending games on time for the release date, but obviously Amazon has got a better price.
Amazon don't really care about customers getting games on release day. They're generally great, but that just isn't on their list of priorities. I've ordered through HMV who tend to be a little better, but a games-specific retailer like Shopto.net are your best bet - they have a guarantee that it'll arrive release day, and they often turn up a day earlier than that. If it doesn't arrive by release date, you get a £3 credit against your next order. Shopto also tend to level-with Amazon on price, and are often cheaper (especially on older games).
Wrong, wrong, wrong, wrong! :) (Bit of Scrubs there). Ever since I order Mario Party 5 back on GameCube, EVERY order for a game from Amazon has turned up on time, on the day of release. Our post where I live is shocking too, deliveries don't come until 2pm some days, so often I wonder if it will turn up, but so far it's not failed me.