Is it possible to access users' search query data? Is it possible to obtain data on what searches have been performed through the front end of a Craft website?

e.g. If there is a search results page which runs

{% set results = craft.entries.search(query) %}


is that the query data stored anywhere? It would be helpful in terms of understanding what kinds of search terms / keywords people are using to search for information.
You could use tracking tools like Google Analytics for this? Otherwise create a plugin that creates entries that keep track of whatever query were used.

https://craftcms.com/docs/plugins/working-with-elements.