All my UI sounds stopped working. Do your other sounds work, like the trash emptying, or calendar alerts?
This problem has been around since at least 2006. Here's a solution that worked for me, from a 2007 thread:
Fire up activity monitor (/Applications/Utilities/) and bring up the processes window (by pressing Apple + 1).
Make sure you sort by 'Process Name' and that 'All processes' are showing (in the drop down list at the top of the window).
Type 'coreaudiod' into the Filter box.
Click on the 'coreaudiod' process shown in the list and click 'Quit Process', then click 'Force Quit'.
It will then restart. This eliminated the problem on my machine without rebooting.
Interestingly, the system then proceeded to play every sound effect that had been missed for the last day or two. I was treated to hundreds of wooshes and blees related to Mail.