IconEditor - Free from Microsoft, an Icon Editor
Microsoft does have a free IconEditor! You get a ZIP file and the C++ code dating from about Windows 95 days.

I discovered it when I was trying to get myself a website favicon and spent hours trying to sort the IE7 favicon bug. No amount of refreshing and deleting the IE7 cache worked for me. What did work was making a 16 by 16 .BMP in 32 bit colour and then converting it to an icon with IconEditor. The final step was to point the browser directly at the favicon. That means type in http://www.gingercatwebdesign.net/favicon.ico into the Internet Explorer address bar.