I forgot my encrypted disk password on OS X

I'm facing the exact same issue. The HD in my MacMini has become corrupted and my only option is to erase it, but, in a fit of security consciousness, I encrypted it with FileVault and so Disk Utility won't erase it at all.

So, not caring about the data on that MacMini (it's just my TV server, nothing that cant be reinstalled and all the actual data is on an external drive) I've booted it in target disk mode (hold down t when you start it up and connect it via FireWire to another Mac) then fire up your Terminal.

% diskutil cs list to get the the Logical Volume Group ID

then run

% diskutil cs delete XXXXXXXXXXXXXXXXXXXXXXXXXXXX <-- put the Logical Volume Group ID in place of the Xs

In my case it said

The Core Storage Logical Volume Group UUID is 48AE3F70-916B-4BEB-AF63-0C2423E1481E
Started CoreStorage operation
Ejecting Logical Volumes
Destroying Logical Volume Group
Error: -69783: Unable to delete the CoreStorage Logical Volume Group

You can safely ignore the error however. When I then fired up Disk Utility there was my disk - newly erased. I will now reboot my iMac in Recovery Disk mode and re-install Mavericks on the MacMini. (Fingers crossed)

Good encryption allows for no recovery. That's how it protects your system from other people.

Encryption sounds like a good idea till you learn to live with it and take extra precautions to prevent the data loss it will force upon you in the event you lose the password. Upon covering all the bases it becomes a useful tool to prevent recovery of data from stolen equipment and not a liability from forgetting the password.

Various other operating systems allow for making a recovery disk or thumb drive when you first encrypt the disk that you can then store in a safe place in case this event happens.

The only recourse is to get it right at least once if you have it written down correctly.