Although I see an option in System Preferences > Notifications to enable applications to pop a sound on new notifications, Mountain Lion is not actually playing those sounds.
Has Anyone run into similar problem?
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I upgraded my mother's new iMac to Mountain Lion and noticed that the mail sending and receiving sounds were not occurring. I found the following URL which was a temporary fix, but the problem comes back... so I think there's a bug here.
You might try the following to see if this helps: