The new mail alert sound in Mail.app was broken when Leopard was released last year. Three updates later, and it’s still broken.
[UPDATE: In deference to posters in the comments below, I should point out that not everyone experiences this problem. It only affects most/many/some/a few users. Like me.]
Fortunately, there is a work-around which you can use until Apple gets around to fixing the problem. It’s a bit fiddly, but not too forbidding.
First download this zip file from Hawk Wings which contains an applescript and the default “new mail” audio file.
Unzip it, and place the audio file in your ~/Library/Sounds folder (where “~” is shorthand for your user directory).
Then open up the script in place the script in Script Editor. You will see that all it does is execute a shell script — do shell script "afplay /Users/timbo/Library/Sounds/NewMail.aiff > /dev/null 2>&1 &". You will need to edit it to replace the name of my user directory with yours.
Then save it in your ~/Library/Scripts/Applications/Mail folder. If you don’t have such a folder, it’s worth creating one.
Now you need to create a rule in Mail.app that triggers the script whenever a new email arrives.
Open up the Rules pane in Mail’s Preferences:

Create a new rule. Call it something creative like “New Mail Alert Work-around” and fill out the rest as per the screenshot. I like to restrict it to people who are in my list of previous senders–it’s a quick and dirty way to rule out being alerted to the arrival of spam. Obviously, there are other ways to select conditions here which restrict when the alert will be triggered.
Also, in the “Perform the following action” field, you will need to select “Run AppleScript”, then navigate to ~/Library/Scripts/Applications/Mail and select the NewMailAlert.scpt that you saved there earlier.
All done. Send yourself a test email, and rejoice. Mail.app is talking to you again.
For extra spice you could use one of the hundreds of mail alert sounds listed at Email Gifs and Sounds
(Or perhaps Scully is more your thing?) but have compassion on your work colleagues. That could get really annoying after a while.
[With thanks to the original posters in an Apple Discussion thread
]

I’ve 
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