System Preferences > Sound > Sound Effects > Play alerts and sound effects through: (what do you have selected here?)
Also, do you have "Play user interface sound effects" checked?
Do you have any sound at all? From other apps etc?
If it is specific to mail.app, then follow the advice in the post above.
* Internal Speakers
* Yes, it's selected.
Yes, all other apps happily chiming beeping and bleeping away.
Boy, I just hate doing a PRAM reset without knowing why or how it will fix the issue. Not saying I won't do it, but I don't like it.
I found this on another board, and it worked for me:
"Success - in the Audio Midi Setup (Applications/Utilities) I changed the output to 2ch - 32bit Float and all the audio works well."
Ever since installing Mountain Lion, my sounds have been missing in Mail UNLESS I restart my computer, after which the sounds will play until I put the computer to sleep. Then they vanish again.
Finally I've found the answer: I unchecked "Enable Power Nap" in System Preferences' Energy Saver menu, both for battery power and AC power. I restarted my computer, and the sounds were back for good.
Doing without Power Nap is a small price to pay; I just have to remember to back up to my Time Machine manually.
I found this on another board, and it worked for me:
"Success - in the Audio Midi Setup (Applications/Utilities) I changed the output to 2ch - 32bit Float and all the audio works well."
System Preferences > Sound > Sound Effects > Play alerts and sound effects through: (what do you have selected here?)
Also, do you have "Play user interface sound effects" checked?