Here's a generic list of activities for systems' administrators - irregardless of platform or hardware (in other words - WAN admins working with Routers and Switches will find this list just as pertinant with a few adaptations as will LAN admins, server operators and P2P power users.)

Periodic sysadmin tasks:

--> Know what is "normal". Note what is not.

Frequent (daily?)
1. Check all systems backup logs
2. Check all systems logs
3. Check all systems security logs
4. Check all systems mail logs
5. Check all systems disk usage
6. Check for CERT and similar announcements
7. Are all machines up?
8. Check UPS status
9. Check tunnel usage report
10. Check Virus Scan rpts
--> Know what is "normal". Note what is not.

Less frequent (weekly or monthly?)
1. Verify that backups are restorable
2. Verify file system structure is valid
3. Check for undocumented system changes
4. Sniff networks for intrusion attempts
5. Check error counts on NICs
6. Check NFS errors
7. Audit router configs
8. Check for disused user-ids
9. Portscan
10. Look for weak passwords
11. Look for overly weak access controls
12. Setuid/setgid audit
13. Check available patches/service packs
14. Recall backup tapes
15. Inspect recalled tapes
16. Check for system or tool updates
17. Performance evaluation/audit
18. Printer audit/test
19. Check Conference Room / Speaker Phone operations
20. Verify system times
21. Check tape supply
22. Update documentation of network, machine configs, processess, other.

Occasional (quarterly to annually?)
1. Verify external DNSs are up and correct
2. Load test network (off hours ONLY) and baseline performance.
3. Global password changes
4. Replace tapes in backup cycles as needed.
5. Cable plant/desktop audit.
6. Update documentation that has slipped.