Search engines are in an arms race to offer better privacy protections to the users, and so far Ask.com is winning, with a promise that "a user's IP address, search data cookie ID and search query will be completely deleted and expunged":
For people concerned about privacy, though, things are looking up everywhere, says reason contributor Declan McCullagh:
These were remarkable improvements. Google, Microsoft and Yahoo told News.com, in response to an earlier survey we did in February 2006, that they kept search records for as long as the data prove useful. Now they've set expiration dates, and Ask.com went further by promising to stop recording user search histories starting later this year. Google also has shortened the lifespan of its cookies from expiring in 2038 to expiring two years from the last visit.
Search privacy is important because our Googling (and Yahooing, and MSNing and so on) provides a unique glimpse into our personalities and private lives. Search terms have been used to convict a wireless hacker and lock up a man charged with killing his wife. Search engine activity is also a fertile growth area for nosy divorce lawyers and employment disputes.
Read about various search engines' privacy policies in their own words here.