Can the alert sound in Mountain Lion's notification center be customized?

Solution 1:

An even better Idea is to got to ~/Library/Sounds and create a sound file with the same name as Basso.aiff and it will supersede Basso without the need for deleting a system sound file.

Solution 2:

Unfortunately, no, you can’t specify different Notification sounds for different apps. That’s the job of the app developer, just like on iOS. There is no “default” sound in Notification Center. It’s all app specific. It’s just that Calendar and Reminders use it for their Notifications. If you don’t like the Basso sound: 1. Go to /System/Library/Sounds. 2. Delete the “Basso.aiff” file. 3. Make a copy of the alert sound you want. 4. Rename the copy to “Basso.aiff.” 5. This will make all apps that use Basso for Notification Center play your chosen sound instead.

^{P.S. Basso is a really awful sound effect
P.P.S. You'll need to restart your Mac for the changes to take effect.}

Solution 3:

In System Preferences, select Sound (on the far right-hand side under Hardware) and then click the Sound Effects tab, if necessary. From there, you can select a different alert sound. Unfortunately, you can only select one sound for all alerts.