In the latest version of the Google toolbar (2.+ go toolbar.google.com to
download) click the Google button and select the Options menu. On the
Options tab un-check the Drop-down search history checkbox.
I think in earlier versions there is a preferences menu option (click the
Google button to display) which will take you to a web page where you can
change these settings.
The following registry key holds the values for the Google Search MRU
HKEY_CURRENT_USER\Software\Google\NavClient\1.1\History
(This may vary depending upon what version of the Google TB you have).