Back up is part of my hosting plan, but when my back up is on the same server as the website and I couldn't access my files I obviously panicked.  What if one day a web host up and folds/shuts down? I really need a back up somewhere else other than the sever the site is on, right?

My host has a separate directory for storing backups but if the server has problems the directory will also be unavailable.  I would get copies stored locally for an emergency.  You will most likely never need it but it is worth having.

I simply download the backup files every few months or after major work so that if there was a catastrophe I have a starting point that is not too far in the past.  Depending on your clients requirements this may suffice.  Mission critical sites with high traffic would most likely be looking at a more expensive automated solution.