I am presently employed as a sysadmin, and I have been for some time.
First, you need to be able to demonstrate serious expertise with an enterprise level OS - Redhat is a good choice, the RHCE is fairly well respected. Many sysadmin jobs require that you are an expert with several enterprise level OSes: AIX, Solaris, Windows, Linux, etc. Then you need to the basics of networking.
Then there could any number of other skills that are required: Oracle, PostgreSQL, Cisco, VMWare, SANs, Citrix, OpenView, Java/J2EE, Checkpoint, LDAP, Apache, SAMBA, Perl, Python, Sharepoint, Exchange, Lotus Notes, etc. I have seen job ads for a linux sysadmin that required senior-level Oracle DBA skills. Some jobs may require a government clearance.
There is no rhyme or reason to IT jobs, they just thrown in everything but the kitchen sink. Here a few recent jobs I have found posted.
Compare these job title to the required skills:
Linux Systems Administrator
Database Administrator (MySQL)
System Admin Linux Red Hat