PenguinPete:
In Fedora 11 and 12, you need to add your user to the "uucp" and "lock" groups. To do so, run the 'system-config-users' utility (or go to system->administration->users and groups), double click on your username, and check off the required groups. Then log out and back in.
If you upgrade to Fedora 12 or higher, you'll need to add yourself to "dialout" as well.
This is all in the documentation under the F12 instructions, I don't know why they don't include the groups for F11 and older...
http://www.arduino.cc/playground/Linux/Fedora