I think the number one skill a sysadmin should have is a solid understanding of shells and shell scripting. The Advanced Bash-Scripting Guide is a good place to start or take a refresher. From the introduction:
A working knowledge of shell scripting is essential to anyone wishing to become reasonably proficient at system administration, even if they do not anticipate ever having to actually write a script. Consider that as a Linux machine boots up, it executes the shell scripts in /etc/rc.d to restore the system configuration and set up services. A detailed understanding of these startup scripts is important for analyzing the behavior of a system, and possibly modifying it.
Not to mention I’ll bet every sysadmin is doing some menial tasks over and over again instead of automating or simplifying them with a script. Sometimes you just don’t realize it. For instance, I can’t tell you how many times I’ve typed a loooong find command to recursively set AFS permissions and I just wrote a wrapper to do it with just two parameters the other day. That one script will literally save me minutes each week. Keep at it and you’ll save hours a week.