Center for Data Redundancy:
Redundancy is the art of duplicating essential components in a system so as to safeguard one of them failing. When it comes to your backups, redundancy means having as many copies of them as possible. When designing your backup strategy, you need to plan for bad things happening. Seriously, the lot—simple drive failure, housefire or flood, inclement storage conditions (heat and humidity do dreadful things to a computer), and so on.
That being said, thankfully, the options for data storage we have available to us today are readily available and varied enough that you should be able to come up with your own way to keep everything safe. At the very least, I'll give you some ideas for where you can keep a spare drive in the case of something catastrophic.
(#) The "single point of failure"
In a system, a single point of failure is a weak spot that kills the system flat if it fails. These are hugely undesirable, because you're putting your trust into a single piece of technology which can fail at any moment. This is why backups are necessary in the first place, because the single point of failure is your computer. If anything goes on it, like the power supply, RAM, a hard drive, at best you'll be unable to retrieve your stuff without surgery. At worst, your stuff's lost.
It's easy to make the mistake that simply having the data on a removable drive is enough, but if anything happens to that removable drive, it's toast. That drive is now your single point of failure. Your security comes from having as many copies as possible of your stuff.
Now, people make their entire careers out of engineering systems to avoid single points of failure. You likely can't escape them. You can, however, avoid it for your data—that being the entire premise behind redundant backups: multiple copies of your files, stored in different places on multiple formats, so that the loss of any one copy doesn't mean the loss of your stuff.
(#) Why multiple formats?
All data storage formats fail. There is no "I copy it to this and it lasts forever" format. The reason I've never appreciated the concept that certain formats are obsolete is that each one fails differently. Conditions and lengths of time that'll kill one format will leave another standing. For long-term storage, they're all useful.
Consider how complex a hard drive is compared to a blank DVD. One contains a quickly spinning (to the tune of 7200rpm these days) metal platter (or several!) and a mechanized arm that magnetizes very specific parts of that platter to store data. Contrary to the single point of failure, there are many points of failure on a consumer hard drive. This contributes to their overall cost and to their reliability, as more things can go wrong in manufacturing.
Meanwhile, optical discs are very thin sandwiches of metals (or in the case of recordables, dyes) and plastics that contains microscopic pits and lands, and depending how the laser beam is reflected back into the player, it can read a datastream off them. (A higher-powered laser can also melt pits onto a disc to store data, in the case of recordables.)
The blank DVD isn't necessarily more resilient than the hard drive, as it too has its specific failure points. Scratches can affect the laser's ability to read the data layer of the disc. The layers can separate thanks to the elements. Bronzing and clouding can occur. If you throw a bunch of CDs in a hot car for years, they'll eventually stop reading. (Be kind to all your media—cool, dark place. Use CD-Rs for the car.)
What the blank DVD does have over the hard drive is its size and that it's much easier to partially recover data from it. Because DVD capacities are so comparatively small, any one disc failing likely means less of your overall data disappearing than an entire external hard drive, as long as you spread things out over multiple discs. I've also gotten files off DVDs with cracks in them, and been able to read just enough of cracked and damaged unmarked CDs to find out what the title was to replace them.
With care, data storage formats can last many, many years, but certainly not forever. In fact, we're really not sure how long these formats last. Not now, not soon, but at some point—you'll need to copy this data off your backups and onto new, fresh media that'll last an additional however many years.
Perhaps by then, we'll have perfected the art of long-term data storage, but it's not today. For now, it's best to keep as many copies as possible on as many formats as possible.
(#) The "3-2-1 plan"
A good nmemonic to remember as far as redundant data goes is the "3-2-1 plan". Under 3-2-1, you keep:
This is a very good start towards keeping your stuff safe. As for what "offsite" means, wherever you store your data, keep one of those copies somewhere else on another property, like your office at work or another house or apartment you frequent. Take care that it's somewhere secure, of course—an offsite backup means you're not there in case someone makes off with your stuff. (Plenty of ways to mitigate that risk—a good lockbox helps, or encrypting the drive potentially.)
Of course, you can always include more copies and more formats in your plan if you want. I maintain a few smaller memory cards alongside my usual two externals for safety copies of my finished work, and the entire somnolescent.net site network gets seasonal backups of absolutely everything, an additional copy of that data being generated every three months.
(#) In summation
Redundancy is the key. You don't want to have only a single copy of anything, stored on a drive that can fail at any moment. You want to copy them out everywhere you can. Diversify your backup media, as they all fail at different rates for different reasons. Store some copies elsewhere in the case of a fire or flood. Remember, any copy is a good copy.
In the next section, I'll discuss various potential contenders as far as backup media goes. Keep an eye out for price, brand, and longevity and don't cheap out. No name backup media will fail on you. Even if someone can pull a disc or two from their own batch on cheap, no name media, it is by no means reliable.