The search engine Ask.com now gives you the option to erase your history using AskEraser:
With AskEraser, people can ensure that their search history will not be retained by Ask.com. Searchers will have easy access to AskEraser and can change their privacy preference at any time. Once selected, searchers’ privacy settings will be clearly indicated on search results pages so they always know the privacy status of their searches.
This is much different than most search engines, who usually use your search results to feed you relevant advertisements.