Today in a post on the Official Gmail Blog, engineering manager Pal Takacsi tells us, "Turn on 'Send & Archive' from the Labs tab under Settings, and you'll see a new button in the compose form labeled just that. The button does what it says: it sends your reply and then archives the thread with one click. For keyboard shortcut enthusiasts tabbing to this new button works, too. In the coming weeks, I'm planning to add Undo support, so if you accidentally archived a thread, you can easily get it back into your in-box."
True to his word, the feature is live in Gmail Labs. I tested it to be sure that it works, and it is pretty flawless. Once you enable the lab, it changes the "send" button to a "send & archive" button. I now have one e-mail successfully archived.
If you're serious about organizing your e-mail, check it out in your Gmail Labs setting.