I don’t want to say you can never have enough back-ups as there is a break even point where you have too many, but you can definitely have too few.
This is not only about genealogy, but applies to many things – photography, writing (blogs, books, etc.), videos you make. It’s best to back-up on a regular basis. Some people do it monthly, but that may not be often enough if you have done a lot during the monthly. Others do it weekly, bi-weekly, daily, and some do it hourly. A good rule of thumb is to back up if you have done a lot since your last back-up. A friend who is an author backs up after so many keystrokes or so many minutes.
Zero back-ups is bad. It may or may not be marginally better than one although I think it would be rare where zero was better than one in most cases. Paper back-up without other online systems in place is also bad. One online back-up is bad even if you have other non-online systems as alternatives. I had a lot of stuff on GeoCities that was lost when they closed the site.
Ideally, you have multiple systems in place – online and offline. For genealogy, you may consider Ancestry, MyHeritage, FindMyPast, FamilySearch, but don’t rely upon only one. Use two or more. I have most of my genealogy stuff on both Ancestry and MyHeritage.
Locally, CDs, DVDs, external hard drive, flash drive, etc. Don’t limit it to only your location. Best to spread backups to other places, and not just around your city. A major disaster could wipe out those in one swoop. Same if you go with only one online back-up.