In Mail.app I have a number of rules that reroute incoming mail to certain folders. The messages sorted into those folders are not particularly important, so I don't like hearing the new mail sound unless the message makes it to my inbox.
I looked at the various actions one can perform for a rule, but there was no option to 'play no sound.' Solution? Open Audacity and generate a one second, 25,000Hz tone and export it as an AIFF to ~/Library/Sounds/. Next add a play sound rule and select the tone (nomailsilence25kHz.aiff seemed logical to me).
Why not just generate one second of silence? Well, Audacity doesn't let you export a completely silent file. 25,000Hz is a frequency well above the human hearing range. Unfortunately, your pets will still receive the new mail notifications.
[crarko adds: I haven't tested this one. I can just imagine the reaction of my dogs to this.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20110208230548664