Right, I did a bit of digging around Apple's support forums. Like Gav says, it seems to be a common bug introduced with either 10.5.6 or 10.5.7.
The fix is to turn on
Play user interface sound effects in System Preferences/Sound.
Don't ask me why, but this does let Mail play the activity sounds, but you have to put up with the crappy sound of things getting thrown in the trash and so on.

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Snaptophobic BloggageHeather Kay: modelling details that matter. "Let my windows be open to receive new ideas but let me also be strong enough not to be blown away by them." - Mahatma Gandhi.