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Win98/ME Users:
C:\Windows\Temporary Internet Files\Content IE5\...
XP Users:
C:\Documents and Settings\%User Account%\Local Settings\Temporary Internet Files
What I do when I spot a favicon on my desktop (which is where I initially drag all my internet shorcuts; I do not use Favorites at all) is pop open my temporary internet files folder, and right-click-drag the favicon to the desktop and select Copy here (one at a time) and quickly rename the icon to match the site name; ie. webmast.ico.
Then I move the favicon to a special folder (Favicons) which I keep in the Shared Pictures folder on my XP. Next, I right-click the shortcut on my desktop and select Properties>>Change Icon.
Navigating to my Shared Pictures\Favicons folder, I locate the icon, open it, then apply it. Finally I drag the shortcut to my Shared Documents\Shortcuts folder and place it in one of the many folders in there, as appropriate. Now I have permanent icons on a great many of my 'favorite' shortcuts and I can find them on the fly when I'm looking for them.
Note: It makes good sense to store all sharable content in the Shared Documents folder. That way, other users have access to the content, as well as the shortcuts.
I've set up several machines for 'newbie' users to default to the Shared Documents with all their apps, and place specially created desktop shortcuts to these folders in every user account. It means quite a lot of work in the Registry, but for them, it's worth it.
But I've stopped using IE so I don't have the need anymore. Might be worth searching to see if you can find something to do this tho.
"FavOrg, scans the Web sites in your Favorites list for favicons and makes your favicons persistent. It also lets you associate any icon you choose with a given shortcut, even if no favicon is provided"
(Actually, to get it free you'll probably have to download it from a different site. But you should be able to find plenty of those with a simple web search for "FavOrg".)