http://www.lifespy.com/2007/web-tip-how-to-clear-google-search-history/

One behavior that you might notice when typing something on the Google search field is that it pops out suggestions from your previous searches. Clearing your history is a good privacy and security measure. Especially when you search all sorts of “stuff” on the family computer. You don’t want your kid brother to come up with your searches that start with “hot” or something.

Google searches are stored as part of “saved forms.” So those are what you want to clear. Here are the basic steps on both Firefox and IE.

On Mozilla Firefox

Here’s what you should do on Firefox:

• Click on Tools -> Options
• Click on the Privacytab
• Click on settings to check and uncheck what you want to clear.
• Check saved form an search history
• Click OK.
• Click Clear Now.
  

Actually, here’s a quicker way using a shortcut.

• Press Ctrl + Shift + Del
• Check saved form an search history
• Click on “Clear Private Data”
  

On Internet Explorer 6

• Click on Tools -> Internet Options
• Click on the Content tab
• Click AutoComplete in the Personal Information section
• Click on Clear Forms to clear the current history
• If you want to disable AutoComplete make sure you uncheck Forms

On Internet Explorer 7

• Click on Tools -> Internet Options
• Click on General tab
• Click on Delete in the Browsing History section
• Click on Delete forms