Patching
There are very few Operating Systems that have an adequate patching process for applications. The only two UBOs we recommend to someone who is too busy to track all of their installed applications is FreeBSD and Debian GNU/Linux. Apparently you can do this with RedHat and its offspring, but I've heard about a lot of issues with "dependancy hell."
It should be noted that "dependancy hell" is usually because the SysAdmin has installed packages from different distributions. For example, installing SuSE packages on a RedHat system is asking for trouble. Packages built for a specific RedHat version almost always work, as do packages rebuilt from .src.rpm files. (RedHat and other RPM-based systems are quite a bit nicer once you learn to roll your own RPM .spec files)
Debian
Using Debian GNU/Linux or any of the ubuntu variants, it's as simple as
apt-get update apt-get dist-upgrade
and all of your installed applications will now be up to date. You can modify where you get your updates from the /etc/apt/sources.list file.
FreeBSD
I've created two shell scripts which I've named update, and upgrade. You will need portsnap, portaudit and portupgrade installed to use these:
#!/bin/sh # update /usr/local/sbin/portsnap fetch