Stale IP addresses clog up your database with useless data, not to mention, may be subject to subpoena by legal authorities in some jurisdictions.
The IP anonymize module helps ensure users' privacy by implementing a retention policy for IP addresses logged in Drupal's database tables. IP addresses are scrubbed on each cron run according to a configurable retention period. For example, you may wish to preserve IP addresses for a short while for purposes of identifying spam.
IP anonymize cannot guarantee anonymity, as IP addresses are recorded at least temporarily, and may also be logged elsewhere in the system such as webserver error logs.
Similar modules: Cryptolog logs ephemeral identifiers—an HMAC in IPv6 notation using a random salt which is stored in memory and regenerated each day—rather than IP addresses. Unlike IP anonymize, client IP addresses never touch Drupal's logs or database tables.