GraphicConverter does not produce 100% compatible .ico icons; I've seen some browsers not displaying them. Specialized icon editors (like Iconographer, IconBuilder, and others) will do the job.
The more proper and more widely supported way is to put a link to your icon in the head-section of your HTML-code:
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<LINK REL="shortcut icon" HREF="img/myicon.ico">
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That some browsers look automatically for a file favicon.ico in the root folder was a quick and dirty Microsoft hack producing more 404 errors in logfiles than actually loading icons. This may (hopefully) not be supported any more in future.
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