i would have to say that my top 10 responsibilities are: (in order of frequency)
1.) Adding/Deleting/Changing passowords and users (changing quotas too)
2.) Deal with a stupid user who blames my network for something not working.
3.) Check the snort logs, and ban those Ip addresses on the router (simple little script kiddie crap most of the time)
4.) Backups. tar mostly, but im a tar kinda guy.
5.) Check the proxy logs for inappropriate access by employees (porn, illegal stuff, etc)
6.) Update/patch everything when an exploit comes out (I don't like running up2date or apt-get automatically, i like to do it manually, because i like to be there in case something breaks...)
7.) Grab data from backups when it is needed/to test medium
8.) Make sure that web/ftp/proxy/file/ssh servers are running well, with plenty of spare cycles and memory on the servers (disk space also)
9.) write scripts to automatically do a number of sys admin tasks (I personally use Perl)
10.) Research new ways to do the same old crap (to save $ on launch, TCO, etc)
I'm more of a client-based sys admin though (In other words, im responsible for about 50 different networks, as opposed to just one. The servers that I do check are done usually via SSH to the remote client). Like everyone else has said, you find different tasks with each job. For instance, I have no freaking clue how to setup a cups server. But, few people have to check NIDS logs, or have to check for future needs of the network. It all just varies. Heck, the same could be said for which distrobution of *NIX people use, it just all depends on the job.