External recovery disk?
Well on 10.7 and above there is a Recovery HD partition on your boot drive and Internet Recovery (newer machines)
https://support.apple.com/kb/HT4718
This method here is used to install OS X on a external drive if you have a messed up boot drive need to perform data recovery efforts.
Create a data recovery/undelete external boot drive
If your boot drive is good and you want to make a hold option key bootable clone, then Carbon Copy Cloner is your baby
Most commonly used backup methods
BTW I don't advise you use Filevault as it encrypts the entire drive and makes fixing your machine a pain, when you really only need a few files secured, can be transferred to another machine and decrypted instead, much safer than Filevault.