Posted to the in-case-you-have-this-problem-too department.
About 6 months ago, Flash stopped playing sound for me. This was terrible: I watch a lot of Flash animations! This aggravated me to such an extent that I went so far as to re-install OSX (which I needed to do anyway, after a semi-botched upgrade to Tiger).
Today, the same thing happened again. Argh! However, this time, I was able to enter in the correct combination of keywords on Apple Support's search page, and found this article:
1) Open Audio MIDI Setup (/Applications/Utilities/), then check the Audio Output setting.
2) Change the Audio Output setting to 44100.0 Hz.
3) Quit Audio MIDI Setup.
It solved my problem! Not sure which Application was the culprit that change that setting to begin with (GarageBand? OS X upgrade?), but I don't care, its fixed!
Update: also mentioned here.