Deleting Search History
Google Videos
If you have a high bandwidth connection see how to clear google and yahoo bar here, and how to clear it in Internet explorer and Firefox.
AutoDelete
Check out the bottom links on the left. Those programs auto delete search history if all else fails.
Internet Explorer
Go to tools>internet options. Delete cookies, delete files, delete history, set delete history to 1 day. Click the content tab, and go to AutoComplete option, then select clear forms. Refer to this
image guide for more details. Also see microsoft's
AutoComplete page.

Disable AutoComplete
You can disable it saving your search terms forever by unchecking all the autocomplete boxes (second picture).
Firefox
Go to tools>options>privacy. Delete cache and cookies. It's also under "clear private data" in newer versions with the quick key (ctrl+shift+delete). Go to the bottom of this page to download the newest firefox.

Yahoo
Click the pencil and click clear history. Click the pencil again and click toolbar options. Uncheck remember recent searches and check IE clears history on close. If you don't have these options download the latest
Yahoo toolbar or delete it by clicking start->settings->control panel-> add/remove programs. See
Yahoo Toolbars' Official HELP Page for more information.

Google
Click the google button and click clear searches. Click the google button again and go to options, then click the search tab. Check out the
Google Toolbar Official Help Page
Get the Latest Firefox and Internet Explorer
If it fails it may be because you have an older version.
Internet Explorer Beta 7Google ToolbarYahoo Toolbar