Many organizations use MailChimp, SendGrid or SocketLabs email integrations to ensure their emails are delivered with whitelisting and lower load on their servers. Switching to Mandrill can dramatically reduce the cost of these services.
Mandrill is a service provided by MailChimp that uses the same email delivery infrastructure as their well-known service designed for delivery to newsletter subscriber lists. Mandrill's pricing is based entirely on number of emails sent, rather than a combination of subscribers and email volume.
One of our clients experienced strong subscriber growth, going from just under 50,000 emails sent a month to a bit under 300,000 emails eight months later. Counting how many contacts were in their various Mailing groups yielded just under 100,000 'subscribers'. This would cost approximately $449 with SocketLabs, $475 with MailChimp, and $275 with SendGrid. With Mandrill, the cost is just $57.60. Quite the savings!
The most recent version of the extension is much more useful since it adds support for CiviMail bulk emails in addition to the 'transactional' emails supported since CiviCRM v4.2. You can now use it for CiviMail and/or other email from CiviCRM.
Look for the extension in your CiviCRM instance, or read more about the extension at https://civicrm.org/extensions/mandrill-email.
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Update: MailChimp changed their pricing for Mandrill so there is an effective minimum monthly payment of about USD$40. As a result of this move, we've been helping clients move to SparkPost, which offers 100k free emails per month. There are two good integrations with it available in the extensions directory.