The situation was that I had 2 Fedora 12 boxen.

One played flash videos with sound, and one did not!

Eventually I found the actual problem, and it was trivially fixed (I don't want to remember the many blind alleys I went into first...).

When I looked at
System ==> Sound Preferences ==> Sound
and selected the 'Applications' tab, I got the line:
"No application is currently running or recording audio.",
but the Mute check box to the right of the 'Output Volume' slider at the top of the tab was unticked.

However, when I was running a flash video, I had a line:
"ALSA plug-in (npviewer.bin) ..." with another Mute check box on the right that was ticked! Unticking this new Mute check box, enabled Firefox to play YouTube video's with sound!

Thanks for posting back the fix!

//NTLB (and marked SOLVED for OP)

Thanks - I had a similar problem on f14 and this got me close.

On mine, my video card's HDMI sound output was set at a higher preference than the motherboard audio (I use a DVI cable to my monitor). In KDE's Multimedia/Phonon control panel, I needed to click on each category, including the root of the settings tree, and select the internal audio and click 'Prefer (Up)' on each.

This was perplexing because system sounds were working, and set to the internal audio, for some reason. The symptom in Flash plugin was the video running at high speed. No need to even refresh the webpage once this setting was re-configured.