How can I remove the pop-down list of previous searches when I start a
new search?  In other words, Google suggests a previous search as I
begin to type.  How can I remove all of these?  Thanks.

The answer depends on which browser and operating system you're using.
 The problem seems to arise most frequently for people using Internet
Explorer with Windows.  In any case, if you follow these links you'll
find some cases where the problem has come up before.  If have listed
several, roughly in order of the answers (or accompanying comments) I
thought were most useful. If one of these explanations doesn't solve
your problem, please ask for a clarification:

http://answers.google.com/answers/main?cmd=threadview&id=172950
http://answers.google.com/answers/main?cmd=threadview&id=123315
http://answers.google.com/answers/main?cmd=threadview&id=98170
http://answers.google.com/answers/main?cmd=threadview&id=193057
://www.google.com/help/faq.html#iehistory

Some of those answers give you explanations of how to prevent this
from happening in the future.

I'd also suggest you look into a small program known as TweakUI.  It
has settings that you can set to delete all sorts of things when you
shut down the computer so that future uses can't see what you've been
up to (just look for the tab labeled Paranoia).  It's free from
Microsoft.  Information on it is in the following article:

Download TweakUI (Annoyances.org)
http://www.annoyances.org/exec/show/tweakui

Best wishes,
Mvguy-ga





Search strategy: 

Google search: tweakui
://www.google.com/search?num=25&hl=es&ie=UTF-8&oe=utf-8&q=tweakui&btnG=B%C3%BAsqueda+en+Google

Google Answers search: delete Google history
http://answers.google.com/answers/main?cmd=search&q=delete+google+history&qtype=all&btnG=Google+Search

See this listing for the answer to your question.  You can also follow
any of the links in the comments section to answer the question as
well.

http://answers.google.com/answers/main?cmd=threadview&id=194899

Comment with answer posted 9:48 AM PDT. Official answer posted 10:04
AM PDT.  Just a note based on a previous thread about answering this
question.