On the 360, you can turn off ALL notifications, but there's no way to select just achievement notifications. This means you will never receive notice of achievements, messages, game invites, etc. If it bothers you that much, it also means ignoring your friends.

On the PS3, you can turn off "notifications" but that is everything EXCEPT for the trophy notifications. There is currently no way to disable those. Heavy Rain is the only game out there that delays the trophies, giving you anything you earned at the end of a chapter, during loading screens, to avoid disrupting gameplay.



Honestly... they're not that annoying. Usually it's out of the way - most games will move the box wherever it needs to go in order to not block the important areas of the screen.