No New Mail Sound 10.6.7
Since you mention this has been going on for years, this is likely related to a longstanding bug in Mail.app and fetching mail with IMAP. Try the instructions here and see if it helps:


  In Mail, open Preferences and go to
  Accounts » Advanced in all your mail
  accounts and turn off the Use IDLE
  command feature. Next, go to the
  General section of Preferences, and
  set Check for New Mail to Every minute
  -- you can set a longer interval if you want, so long as you don't set it
  to Manual.
  
  Now your mail alerts should play for
  every incoming message, but you will
  see your messages up to one minute
  later than you would with the IDLE
  mechanism.