When running Fedora 10 under Gnome, there is no method available in the GUI that lets you enable automatic login. Instead you need to open a terminal window and edit the /etc/gdm/custom.conf file (you may need to su to root before you can edit this file).

Once the file is open, add this to the bottom of the file:

[daemon]
TimedLoginEnable=true
TimedLogin=YOUR_USER_NAME
TimedLoginDelay=0

Obviously you'll want to change YOUR_USER_NAME to the name of the user you want to login. Save the file and next time your machine is rebooted, it'll automatically login as this user.

I'm not positive, but I'm also pretty sure this will work in Fedora 9 and Fedora 11. I know it doesn't work in version of Fedora older than Fedora 9.