The iPhone,iPod touch, and the iPad do not support flash. Youtube is accessible via safari on the aforementioned devices as it will load the mobile version in which every featured video is optimized for mobile devices that do not support flash. Also like Dweez said there's the youtube app, which is how the videos will be played anyway if accessed via safari.
As far as Safari on a Mac, as obvious as this may sound perhaps there's a missing plugin? Also, one time i had a very similar issue with firefox and it turned out that clearing my cache was a quick fix.
I realize this is an older post but what the heck.