For those who are not aware, Adobe have finally "officially" released their native 64-bit flash plugin, which is great news for 64-bit Linux users.
See here for more info - http://www.adobe.com/products/flashplayer.html
The Fedora 16 (64-bit) how to
Feel free to use your browser to download the plugin, visit the download section in the above link. I recommend using the yum repo in Fedora if you wish to receive updates automatically.
But for those who like the terminal....
su -c 'yum install http://linuxdownload.adobe.com/linux/x86_64/adobe-release-x86_64-1.0-1.noarch.rpm'
su -c 'yum install flash-plugin.x86_64'
That's it, enjoy native 64-bit flash in Fedora 16!
Edit: Updated to reflect comment made by Rags, thanks for the advice.