Tom uses MailChimp which can be used in conjunction with WordPress sites among other things. It is independent of WordPress.
If you want something integrated with WordPress and not stand alone like MailChimp then I would recommend MailPoet.
Either do a pretty nice job. I prefer MailPoet because i find it very easy to understand.
If you want to keep your database as small as possible then look at MailChimp.
Hope that helps.