How do I mute event sounds in Adium?

The no-sounds-ever solution

Go to Preferences→Events, and remove the sound action (“Play sound ‘NewMessage’”) from every event that has one. You can see the actions assigned to an event by clicking the disclosure triangle at the left side of the event's row in the list of events.

If you're using one of the built-in presets, you'll need to create a new one. Adium will prompt you to do this when you try to delete one of the actions. Simply click OK (optionally giving a name for the new preset first).

The one-status-at-a-time solution

If you want to keep the sounds, but only for certain statuses (or, more exactly, only not for certain statuses), you must create a custom status.

Go to Preferences→Status. If you want to mute sounds in an existing status, double-click on it, check the box, and click OK. If you want create a new status with sounds muted, either select a status from the Status menu with the Option key down, check the box, and check “Save Custom Status”, or use the + button in the Status preferences.