Information saved locally is the main way sites such as google identify you (cookies mainly).
If you open an incognito window for all your searches, do not signin and close it right after, search engine will not associate your searches with you.
This is not enough to protect you from an evil company or government, but will affect which ads are presented to you, your search results, and should prevent your name from being associated with those searches should that search company date be compromised.
