Just in case you are unsure about how to enable or configure these features, anniversaries (and birthdays) are added by the Cakeday plugin, the Leaderboard is added by the Gamification plugin. The badge system is a part of the core Discourse code. It can be configured from your Admin / Badges page. Let us know if you have any questions about setting things up.
It would be great to hear from some sites that are making use of these features. I know they’re out there, but are not necessarily active on this forum.