Unless you're using a real backup system, onsite to external hard drives isn't a "back-up" solution. Even if you copy it multiple times, all you're doing making your process more complex than a back-up solution should be and increasing your chance of failure. Drives fail, there's no two ways about it. IMO, for a true back-up solution to be successful, it has to happen automatically without your intervention. I have multiple copies of my data locally, but I wouldn't consider that a back-up solution. As mentioned, you need to pick one that has a reputation and will be around when you need your data. There's three that I would trust, pick which one works for you. I would trust mozy, carbonite, and back blaze. I'm using back blaze. The thing I liked about back blaze is they allow you to backup external drives to their cloud, they allow access to your files via any number of ways (mobile, other computers, mac, pc, etc) and their cost is reasonable. Be careful with a lot of the review sites, I found a large number of them are put up by the various back-up companies or the reviews are paid advertisements for the various back-up companies.
Keep in mind I have a cabinet at a data center downtown that I could very easily "back-up" to but again, it's more cost effective to let the pros deal with the backup and redundancy that's needed for a solution to work.