Ash HN: How do you monitor success/failure of your overnight backups?

In our company we have several servers that we are backing up regularly. All backups are copied on a single machine and from there they are copied off-site.

Depending on the server and data type backups are sometimes database dumps (or wal files) or just filesystem rsyncs, or just tar archives of a directory - mostly overnight backups but for some databases we make hourly dumps. At present moment I occasionally check that each backup directory on backup machine contains the latest (today's) archive files. Ideally, I would like to have an automated system that checks each of the predefined directories on a backup machine for today's files and if they are missing (which means that the backup failed) to send some kind of alarm. Is there a solution of that kind or if not, what are your strategies for ensuring that backup is running without failures?