Facebook - Search History will be kept in Activity Log
While only the individual user can see this, sharing your password or hackers compromising an account could create some privacy concerns.
QUOTE: Facebook announced yesterday that they will now be adding user search history to their Activity Log. The Activity Log was released along with Timeline late last year and is a useful tool that allows you to quickly review and manage your Facebook activity. Quite a few bloggers have posted some sensational headlines about this new feature. First off, only you can see your Activity Log. Unless you let other people access your Facebook account you really don’t have anything to worry about. If your account is hacked, you probably have bigger problems than a hacker viewing your search history.