Fedora, Red Hat Enterprise and CentOS systems (and possibly more distributions too) ship with a tool called Logwatch. Logwatch is absolutely invaluable if you're running a server of any kind as it allows you to stay up-to-date with what's going on inside your system.
As the name suggests, it watches the system's log files. Every day it will send you a digest email containing bits of information from the logs around your system. This makes it nice and easy to check up on what your system has been up to without manually trawling through your logs.
By default, Logwatch sends email reports to the root user on your system. To read them, you'll need to become root, then run the mail command to enter your email system (if you've configured a different MTA, then use that instead of mail).
$ su -
[[enter your root password when prompted]]
Once in the mail interface, enter a number and press Enter to read the corresponding email (if you have any). Logwatch emails will be clearly identified as such in the subject line. You can scroll through and read your email using space, Enter or Page Down. When you want to quit out of the mail interface, type q at the prompt. (For more information about using the mail interface, try man mail)
Logwatch where set up will send one email every day with a summary of the latest changes. If you remember to check your mail as root daily, you can easily see what's going on with your server! Logwatch is a great tool that ships by default with Red Hat-derived distros and a lot of people don't realise it even exists. When you're running a server, it can prove to be very useful.
If your distro doesn't ship with Logwatch, search in your package manager and choose to install it.