How can I delete search queries from the pull-down list, not only
future ones, but those that already exist?

In Internet Explore, this feature is called Auto Complete.  You can
disable this feature for all future sessions (and prevent the pull
down list from ever appearing again) by going into the Tools menu,
clicking Internet Options, then Content.  Click the AutoComplete
button.  Deselect the Forms checkbox, and also click the Clear Forms
button to erease the existing data.

In the Google Toolbar, you can prevent previous searches from being
viewed by clicking the Google icon on the toolbar and hitting the
Clear Search History button.  That will delete existing data.  To
prevent further data from being obtained click Options.  Click the
More tab and deselect the Save The Search History Across Browser
Sessions.  That should do the trick :).

-Matt