Sometimes it’s the simple things… Apticron is a great little tool that will send you an email once a day (depending on your Linux distribution) if there are updates available. So you don’t have to login to your server regularly just to check for updates.
Install it, e.g. via apt-get install apticron. Then edit the configuration file /etc/apticron/apticron.conf and set your email address
If you don’t want to get reminded daily of available updates enable DIFF_ONLY. You will then only receive an email if there are additional new updates.
Starting from version 1.1.51 you can also set the sender address (From: address) by setting CUSTOM_FROM.