The Google search page on my computer maintains a history of previous
searches.  All prior searches can be seen when the cursor is placed in
the box to enter any new search word(s).  To the many people who use
this computer but value their privacy, this is unacceptable.  How can
I delete the existing scroll down list and prevent a new one from
being compiled?  This question has probably been answered by you and
is perhaps even available in Google Help but I'd appreciate an answer.
 thanks.

I am assuming you are using Internet Explorer 5.0+. IE has this
annoying feature built in called "Autocomplete" which aims to finish
forms for you such as addresses, usernames, etc.

To turn this feature off, open an Internet Explorer window, and click
on the "Tools" menu, then "Internet Options..."  A window titled
"Internet Options" will appear. Click on the "Content" tab near the
upper center part of this new window. Next, click the "AutoComplete"
button towers the lower right portion of the window. Uncheck all of
the boxes for "Forms", "Web Addresses", and "User names and
passwords". This will stop new entries from being logged.

In addition, to clear the past entries, click both "Clear Forms" and
"Clear Passwords" to clear any past searches and password entries
users of this computer may have used. This should solve the privacy
issue. Please ask me to clarify these instructions if you are lost!