You can leave the birthday calendar option enabled in Mountain Lion’s Calendar (previously iCal) but shut off the audio alerts option. That way, birthdays from your Contacts and Facebook friends can be seen, but not heard.

In Calendar, the option to toggle the Birthdays calendar is under Calendar > Preferences > General. If you turn it on, you can right-click the new calendar that appears in the sidebar, choose Get Info, and choose the “ignore alerts” option in the sheet that appears.