Sometimes you want to be alerted when you have new e-mail, but you don't want an audible alert. Here's how you can do it.
If you take a silent audio file, when you install it as a new silent ring tone and set it for the New Mail alert, your phone will vibrate only. Since the iPhone lowers any audio currently playing, you want to make this as short as possible (.1 sec), so the audio dip will be at a minimum.
[kirkmc adds: It so happens that I have a bunch of silent MP3 files on my website, in an article about adding silence to iTunes playlists. I added a .1 second file, as well as a .1 second ringtone to the zip archive.
I set up the ringtone on my iPhone, but I wasn't able to test if it works or not. I happen to be part of the 1%; that is, the 1% of people whose iCloud e-mail has been down for more than 24 hours, and none of my other accounts work with push e-email.]
Mac OS X Hints