I've turned off almost all notifications on my iPhone. No email sound or vibration, no Twitter popups, nothing from Facebook -- even if it worked, nothing from Ping -- if anyone used it, no Game Center trumpets, no nothing. Almost. I do leave on SMS and Phone (because I need working telephony), and Calendar and Alarm still get to alert me (because I need to stay employed). That's it.
But it used to be the opposite.