This XenForo 2.x addon sends a summary of XenForo logs to administrators via email. Currently only server error logs are implemented. This runs using a XenForo cron task and can be configured to check for new log entries on a fixed interval (minimum 5 minutes). So you could have it send a...

Sends an email to your members every day showing most popular topics. By default all members will receive a Daily digest. If a member does not want to receive the Daily digest, they can unsubscribe by clicking the link provided in the visitors tab. (Example of Daily digest email) (Example...