Jon Tejnung

This plugin will give you three alternatives for managing your WordPress updates:
<ul>
<li>Update automatically – This updates WordPress/themes/plugins automatically and sends an email to the site admin when an update has been performed.</li>
<li>Update automatically (no email) – Same as the first alternative, but without the email.</li>
<li>Inform about updates once a week – This will send an email to the admin once a week if there are anything that can be updated.</li>
</ul>
Notice that only plugins/themes that resides in the WordPress 
repository will be updated/informed about.
The plugin has not been tested and is not primarily made for multi site-installations.

Simple Automatic Updates

Activate automatic updates or weekly notifications for the site.

Alley

Scott Cariss

Monitors your WordPress installation for core, plugin and theme updates and emails you when they are available. This plugin is ideal if you don’t login to your WordPress admin regularly or you support a client’s website.
Features
<ul>
<li>Set the interval of how often to check for updates; hourly, twice daily or daily.</li>
<li>Sets WordPress to check for updates more often meaning you get to know about updates sooner.</li>
<li>Get emailed about core, plugin and theme updates.</li>
<li>Chose if you want to be notified about active only themes and plugins updates.</li>
<li>Remove upgrade nag message to non-admin users.</li>
<li>For advanced users there are a number of filters and actions you can use. More coming soon.</li>
</ul>
This plugin is a fork of <a href="https://wordpress.org/extend/plugins/update-notifier/" rel="ugc">Update Notifier</a>. This plugin was forked because there seemed to be no further development on the existing plugin and there was no way to contact the original author to ask about taking ownership. WP Updates Notifier has the following improvements over Updates Notifier:
<ul>
<li>Completely rewritten from the ground up using best practises for writing WordPress plugins</li>
<li>Code wrapped in a class so better namespace.</li>
<li>You can set the cron interval, allowing for more frequent checks.</li>
<li>Update checks trigger WordPress internal update check before notification.</li>
<li>Allows you to set the ‘from address’.</li>
<li>Allows you to set multiple ‘to addresses’.</li>
<li>Makes use of the Settings API.</li>
<li>A number of available hooks and filters for advanced users.</li>
<li>Active support and development.</li>
</ul>
Languages
<ul>
<li>French by <a href="http://www.ordilibre.com/" rel="nofollow ugc">Christophe Catarina</a> – Added 03 July 2013</li>
<li>German by <a href="http://alexander.pfabel.de/" rel="nofollow ugc">Alexander Pfabel</a> – Added 02 October 2012</li>
</ul>
<h3>Filters</h3>
Two filters have been provided to allow you to alter the email subject and email content being sent by WP Updates Notifier.
<h4>sc_wpun_email_subject</h4>
@parameters: 
$email_subject – the email subject to be filtered.
Example:
<pre><code>/* 
* Alter the email subject being sent by WP Updates Notifier 
*/
function alter_wp_updates_notifier_email_subject( $email_subject ) {
 $email_subject = 'This is the new email subject for updates notifier';
 return $email_subject;
}
add_filter( 'sc_wpun_email_subject', 'alter_wp_updates_notifier_email_subject' );
</code></pre>
<h4>sc_wpun_email_content</h4>
@parameters: 
$message – the content of the email to be filtered
Example:
<pre><code>/* 
* Alter the email content being sent by WP Updates Notifier 
*/
function alter_wp_updates_notifier_email_content( $message ) {
 $message = 'This is our new email content that will override the default.';
 return $message;
}
add_filter( 'sc_wpun_email_content', 'alter_wp_updates_notifier_email_content' );
</code></pre>

WP Updates Notifier

It's ok for theme and plugins notifications, but notification about core updates does't work for more than one year!
This plugin probably won't recieve an update anymore.

Out-of date and not fully working

Sends email to notify you if there are any updates for your WordPress site. Can notify about core, plugin and theme updates.

Simple Automatic Updates vs WP Updates Notifier