This site has taken significant steps to protect your privacy. It should remain this way, given the operating model is not based on advertising or collecting personal information for sale to advertisers.
There are no cookies at all for most of this site.
There is however one cookie used during the "Add Site" and "Manage Site" workflows. This is called "session" and is just used for preserving state between requests to improve the experience. As it's name suggests, this is a session cookie rather than a persistent cookie, so is deleted as soon as you logout or close your browser.
No files are downloaded from third parties, so there is no opportunity for third parties to track your use of this site.
No personal information is gathered while searching on this site.
In the "Add Site" and "Manage Site" sections, site owners are asked for their site's admin email address. This is so that they can be notified about important changes to their listing, e.g. if their listing was about to expire. Note that the admin email address for a domain is often a shared account, e.g. firstname.lastname@example.org, and is sometimes publicly available via whois, so is not necessarily personally identifiable information.
There are no client-side analytics. There are server side logs which contain search queries, and those may be periodically reviewed to help resolve issues or improve the service.