comparison of email newsletter oriented modules: https://www.drupal.org/node/645108
Mime mail, https://drupal.org/project/mimemail, can also replace the standard Drupal mail so that all your administration mail, registration confirmations, and everything else, is themed the same way as your site. Some other mail modules (such as Simplenews) uses Mime mail to format and send mail.
simplenews (drupal module): Simplenews publishes and sends newsletters to lists of subscribers. Both anonymous and authenticated users can opt-in to different mailing lists. HTML email can be sent by using Mime Mail module.
Newsletter module aims to be a full blown newsletter solution for Drupal 7. It is especially recommended for people that need more than one newsletter list for their site.
The MailChimp module, https://drupal.org/project/mailchimp, connects to the external MailChimp service at mailchimp.com. You would use an external service if your Web host limits your email activity. MailChimp has an easy to read Web site and a million users. The service is free up to 2000 subscribers and 12000 email per month.