All engines do save queries. I don't believe there's much hope of seeing any engine renounce to this data opportunity.<p>Users though, could keep better track of their queries and selected results. Saving this data locally on their machine is an option. This is useful for recall, but also allows to share queries and results with others. The latter allows to build various result and query recommenders.<p>For instance, <a href="http://www.seeks-project.info/" rel="nofollow">http://www.seeks-project.info/</a> lets you share your queries with others so you can benefit from their work on the results. You can play with it by using the demo server <a href="http://www.seeks.fr/" rel="nofollow">http://www.seeks.fr/</a>
I don't know their official answer, but the value of the information FAR outweighs the cost to retain the data, so you'd have to assume they do. Their entire businesses are built upon their ability to use what they know about their customers to generate revenue, and the terms a person has searched for are a component of building this profile.
<a href="https://duckduckgo.com/" rel="nofollow">https://duckduckgo.com/</a> saves your search queries, but does not ever log the IP address of the machine doing the search, nor any unique identifier which could link searches together. See <a href="https://duckduckgo.com/privacy.html" rel="nofollow">https://duckduckgo.com/privacy.html</a>
Of course they do. They even let you see your search history: <a href="https://www.google.com/history/trends?hl=en" rel="nofollow">https://www.google.com/history/trends?hl=en</a>