Gnome Windows Environment
System--Preferences--Internet and Network --Remote Desktop
After the "Ask you for confirmation" is unchecked, I could connect the Fedora from Windows 2003 by VNC Viewer without password.
KDE krfb Desktop Sharing
System Tools --krfb Desktop SharingClick on Configure... button
Uncheck "Confirm uninvited connections before accepting
Check "Allow uninvited connections to control the desktop"
By vncviewer downloaded from http://www.realvnc.com, I could connect to my Fedora without authentication.