Recover a broken or damaged database from the transaction file or "journal"
The MySQL binary log is what you are looking for. Aside from being used for replication, because it stores a range of writes executed on the server, it can be used for point in time recovery. 

You will need some kind of regular starting point in case of recovery (such as a full backup), and then you can use the binary logs and mysqlbinlog to roll forward to an arbitrary point in time (e.g. just before an accidental table drop). So they won't substitute backups but can complement them nicely.

Some people was able even to use them to roll back actions under specific circumstances and configuration.