It can sometimes be a little bit tedious to find the “shortcut icon” link in the HTML. Another approach is to create an Internet shortcut (i.e., a “Favorite” in IE, a.k.a. a “Bookmark”) and open it with Notepad:
[DEFAULT]
BASEURL=http://superuser.com/questions/532616/grab-favicon-ico-…
[]
Prop3=19,2
[InternetShortcut]
URL=http://superuser.com/questions/532616/grab-favicon-ico-using-google-…
IDList=
-> IconFile=http://cdn.sstatic.net/superuser/img/favicon.ico
IconIndex=1
The IconFile and IconIndex are usually at the end.