I've installed Ubuntu Gutsy on multiple systems, and they have all had the same issue, the flash player does not work. After installing the non-free Flash player, going to a site like youtube will show you an error saying that you don't have the latest flash, or you need to turn Java on.
A notification is also given to install the missing component, which is of course already installed.
thanks to formal, who directed me to the solution on the Ubuntu forums...
from https://answers.launchpad.net/ubuntu/+question/19584 - Cyrus Jones said:
"... Using Synaptic Package Manager, remove the package flashplugin-nonfree ...
Then just download this package (32-bit only) and install it (it is identical to the current package in the next release of Ubuntu, Hardy 8.04): http://launchpadlibrarian.net/107610...untu2_i386.deb "
this has fixed it in many instances for me.