How can I allow users to receive e-mails whenever I update my blog in Drupal 7?
This can be acquired easily. I can give you some steps to follow.

There are actually at least 2 ways to achieve that

A. Using Triggers (core module)


First activate the core module Triggers. This will provide you basic triggers (in your case UPDATE trigger) and actions to run when condition is met.
Go to Admin > Configuration > Actions then CREATE AN ADVANCED ACTION, then select: Send e-mail. In the recipient field you need to select a proper token provided by simplenews module to match all the registered users. (make sure you also have Token module installed)
Go to Admin > Structure > Triggers, then Node tab. Choose the third: TRIGGER: AFTER SAVING UPDATED CONTENT.


If you need more control then implement the hook

function YOURMODULE_trigger_info_alter(&amp;$triggers) {
 //Here dpm($triggers) to see where is your update trigger and do the changes.
}
?>

B. Using Rules (contrib module)
Basic the same thing. If you get stuck follow these steps on a similar issue 
on this blog:
http://adellefrank.com/blog/how-to-email-notifications-comments-drupal7