System--Preferences--Internet and Network --Remote Desktop
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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 Sharing
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Check "Allow uninvited connections to control the desktop"
By vncviewer downloaded from http://www.realvnc.com, I could connect to my Fedora without authentication.