A service like crashplan or backblaze should largely take care of that for you. Unlimited incremental backups for a fixed monthly fee. If you discover a file has been corrupted, you just go back in the incremental versions until you get to a good copy. If $5/month is still too much, you can even point it at one of your own machines. You still get the incremental backups; you just have to provide the storage space.

Either way, the key is not just to have multiple copies of the most recent iteration of a file, but to have an automated system of archiving past versions - of everything - as well.