Backup

Check DB12 for last successful backup

Disk space

Run df -k on OS level for amount of free space on volume level

Tablespaces

Check DB02 for Status and usage of Oracle Tablespaces

SAP System Log

Check SM21 for errors

Updates

Check for update records in SM13

Shortdumps

Check for ABAP Dumps in ST22

Enqueue

Check for Enqueues in SM12

Jobs

Check for long running jobs

Workprocesses

Check SM51 SM50 for number of systems/ work processes active