It's not Google that remembers this, it's your browser.
Firefox: Tools -> Options -> Privacy -> History -> "Remember what I enter in forms and the search bar" has to be OFF (check the Private Settings options a bit further on that page to clear what it has saved at the moment)
Internet Explorer: Tools -> Options -> Content -> Personal Information: Autocomplete -> Use AutoComplete for Forms has to be OFF (and click the "Clear Forms" button while you're there to get rid of everything it has saved at the moment)
― StanM (StanM), Tuesday, 2 January 2007 22:50 (seventeen years ago) link