How do I remove or clean up the alphabatized list on Google that automatically
appears whenever I type in information in Google to do a search?

Greetings, noelwood!

If you are referring to deleting the Search History list from the
Search Text line in the Google Toolbar, here are the instructions:

"2. How can I clear my search history? 

If you want to clear your previous searches from the drop down text
box:

Click on the Google logo to access the drop down menu. 
Choose the Clear Search History option. This will clear all the
previous searches out of the drop down box.
Note: this clears your Toolbar's search history, which is different
from clearing your browser's search history. To clear your Internet
Explorer browser's history:

Click the browser's Tools menu. 
Select Internet Options... (the last entry in the list). 
Click the General tab. 
Click the Clear History button. To completely disable the history
function, change the "Days to keep pages in history" to 0 (zero).
http://toolbar.google.com/faq.html#history


If you are referring to deleting the Search History list from the
Address Line of Internet Explorer, here are the instructions from
Microsoft -- applicable to Internet Explorer versions 1.0 through 5.5.
Note that these instructions also work for Internet Explorer 6.0:

"Internet Explorer 4.0, 4.01, 5, 5.5

In Internet Explorer, click Internet Options on the View (or Tools)
menu.

On the General tab, click Clear History.

Click Yes, and then click OK."
http://support.microsoft.com/?kbid=157729


Search Strategy

deleting internet explorer history
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=deleting+internet+explorer+history&btnG=Google+Search


Before Rating my Answer, if you are using a different browser, or if
you have problems in deleting your Search History, please post a
Request for Clarification, and I will see what I can do for you.
    
I hope that this Answer provides exactly the information that you
needed!

Regards,
         
aceresearcher

Try this:
In internet Explorer select the tools drop down menu, and then select
Internet Options.  Click on the content tab, and then click the
Auto-Complete button.  Click the Clear Forms and Clear Passwords
buttons.  This will solve the problem you have been having.