To get information about the behaviour of my visitors, I use Ackee. This analytics software gives me general insight about visitors, but does not track visitors, and does not store any personally identifiable information.
Go to their documentation to find out what Ackee collects.
To get information on how well my site is performing, as well as capture any errors so that I can resolve them, I use a self-hosted instance of Sentry. I do not store any personally identifiable information, and any information I do store I remove after I've resolved the issue.