You can do the following activities as mentioned below:
1)Check all the Databases are Up
2)Taking the Backups of the Databases
3)Verify the Backups taken
4)Monitoring the Users Intrusion
5)Checking the Alert Logs
6)Monitoring the Performance Statistics
7)Usage of space in different Tablespace
my problem is i solve the problem which come on a daily basis but still some tipical problem that will comes very rarely even for after a year or once in a life.
I am here perform all the routine work like taking backup, checking tablespace, tuning a database, application tuning, checking alert log but apart from this type of problem is there any major problem arise for that u must have to contact for oracle people having very very sound knowledge.