This feature was added to the Xbox 360 in a Fall update in 2006 but some new users may have missed this.  I prefer this feature because I do watch a lot of movies on my Xbox 360 and find it annoying to always get those notifications.

On your Xbox 360 controller press the jewel button in the middle of your controller.  Then select Personal Settings from the blade that slides onto the screen.  From there select Notifications.  On Notifications you can choose to not receive notifications,  not play a sound or to not display notifications during video.

I have all notifications turned off while watching a video.  I prefer to have this setting always on so that in case I forget to set my online status to busy I don't see that Chain5awBabe or someone else on my friends list has signed on or sent me a message.   So if you use your 360 to watch movies like I do, this really helps enjoy the movie experience.