If you use yum to manage your server's packages and you're trying to keep things stable then only installing security relevant fixes makes a lot of sense. The yum-plugin-security package adds a plugin that makes keeping track of these things a snap:

yum -y install yum-plugin-security  

Then you can list the errata that are available for your system:

yum updateinfo list  
Loaded plugins: fastestmirror, presto, refresh-packagekit, security  
updates/updateinfo                                                                                                                                           | 1.2 MB  00:00:02  
FEDORA-2013-9851  bugfix      ModemManager-  
FEDORA-2013-10428 bugfix      NetworkManager-glib-1:  
FEDORA-2013-8722  bugfix      PackageKit-0.8.9-1.fc18.x86_64  
FEDORA-2013-8722  bugfix      PackageKit-device-rebind-0.8.9-1.fc18.x86_64  
FEDORA-2013-8722  bugfix      PackageKit-glib-0.8.9-1.fc18.x86_64  
FEDORA-2013-8722  bugfix      PackageKit-yum-0.8.9-1.fc18.x86_64  
FEDORA-2013-8722  bugfix      PackageKit-yum-plugin-0.8.9-1.fc18.x86_64  
FEDORA-2013-7532  bugfix      Thunar-1.6.3-1.fc18.x86_64  
FEDORA-2013-16676 bugfix      abrt-2.1.7-1.fc18.x86_64  
FEDORA-2013-20279 bugfix      abrt-2.1.9-1.fc18.x86_64  

The type of errata can be listed:

yum updateinfo list security # could also be bzs, cves, etc  

To update to the latest version of packages that a fix security issue use the following:

yum --security update-minimal  

If you use the following:

yum --security update  

You'll get the latest version of each package that has a security fix, even if that latest version doesn't fix a security issue.