Few routine tasks are:
1) Event viewer check
2) Manual Virus/Trojan scan and if that’s done automatically, review of logs
3) Disk Defrag (weekly will be fine)
4) Run the Task Manager and check for presence of any illegitimate processes…if a root kit is there, then an AV or trojan scanner may not be able to detect it
5)Also check logs of whatever application installed; for eg. if mail server is there, check logs to see if the mail flow is smooth, its not compromised etc.
6) Verify backups of system state