I have IE6.0.  Sometimes I notice that "My Computer" is listed when I
click on the "History" tab and lists things that I've done through "My
Computer."  Is there any way to keep IE from listing things done
through My Computer in the History?

IE and windows explorer are now basically the same thing. You cannot
do what you are requiring.

usrhlp.

If you are talking about the drop-down list for the address bar,
normally IE only shows web URL history when viewing a website, and
local folder history when viewing a local folder.

If I use IE to open an HTML document that is stored locally, I won't
see any websites in the address listing, only other folders.

That said, I don't know how to change it if this isn't working.  Maybe
it's based on what "zone" IE thinks it is looking at, or maybe there
is just an option for it somewhere.

Sometimes temporary files and history information stored by IE gets
messed up and does weird stuff.  Try deleting your temporary files and
history if you have not already.