Well that's pretty open-ended....
In no particular order, here's some of what I like to run:
> You list "backups", but that will likely be at least 3 different jobs/schedules for FULL, DIFFERENTIAL, and LOG backups
> I have a job that looks for failed Agent job steps and reports them to me, as a check on Agent jobs
> I have a series of daily checks in one job: Autogrow events in the last 24 hours, critical DB sizes, DBs in FULL recovery mode that aren't in a specific list of DBs that should be, etc.
> TempDB size tracking
> Purge old records from msdb for things like backup runs, etc.
> Find SQL backup files on disk that haven't gone off to tape via a network backup. This took a bit of work with CLR for me to set up, but I can now easily query the SQL backup drive for *.BAK files that have an archive bit set, which means they haven't been backed up to tape by our system backups.
Does this help?