A pair of external hard drives
So you've done everything right, you bought an extra hard drive for storing your files from your laptop to save local space and to keep files you don't access often stored somewhere else. Unfortunately, this isn't always enough. Though it's fairly rare, hard drives do fail. Sometimes it's due to overuse, other times it's due to misuse (like not properly ejecting your drive, or simply dropping it a few too many times). Also sometimes drives just fail. What ever the reason, it really is best practice to store a second copy of all of your precious files just in case.
As inconvenient as it is, the best solution here is to buy external drives in pairs. One drive can store the files in an unarchived (or unzipped state) for easy review, while the second drive might store files archived with an archiving utility. As time goes by you may find certain archives aren't necessary to store, letting you pair down your file storage needs. Unfortunately, if you hope to keep ALL your files safe forever it's likely that over time you'll need to continue to pick up those external drives two at a time.
Saving space via archiving
It's likely you already know what a ZIP file is, but let's just go over the basics. ZIP files allow a method of compressing files down in size and combining many files into one more manageable file. If you're a user of Windows, Peazip does a great job of archiving files using ZIP and a number of other file compression methods. Meanwhile, on your Mac, you can simply select a group of files or folders, and select compress from your file menu in the finder. Archiving your files via a compression tool makes dealing with all those files a bit more manageable in terms of both storage and dealing with files by the thousands.
Dock and store
Another slightly more affordable option (in comparison to external drives) is to pick up a hard drive docking enclosure. This handy device, usually connecting to your computer via USB, lets you use internal hard drives like you would an external drive. You simply plug an internal drive into the dock, and the drive mounts like any external drive. Since often internal drives go on sale, buying a docking enclosure lets you pick up multiple drives without having to own a massive desktop tower to store them in.
If you're going to be storing external drives outside of a PC or enclosure, consider picking up some cases for safely storing drives on a shelf or in a drawer.
Build your own portable enclosure
Similarly, you could also pick up a external enclosure which lets you build your own portable USB hard drive. A standard 2.5" or 3.5" drive is assembled (by you) into the custom enclosure (often with an accompanied power supply), and once the drive is mounted and formatted properly (more on this here) the drive can be used like any other.
For use as a backup, simply shelf your hard drives as you fill them, (of course as above, never storing the only copy of a file on one disk) and pick up a new drive for assembly with the enclosure for use as needed.
RAID (or Redundant Arrays of Inexpensive Disks)
Though perhaps a bit complicated to discuss in length here, RAID (or Redundant Arrays of Inexpensive Disks) is a professional solution which is often used for storing backups. In a RAID setup, a group of drives is configured to work together, allowing for higher performance, and in some cases greater redundancy. In certain configurations, a RAID setup can protect your files allowing, one of a group of drives to fail without effecting the data.
Though this is not for the timid, it's likely you know someone who has taken then time to set one up. Ask around and see if a RAID solution might suit your file storage needs.
Built into Mac OS is Time Machine, which lets you schedule automatic backups of your drive so you can revert back to an earlier date if your system becomes corrupted. This unfortunately doesn't help you much if there is a critical issue with your system drive, but it's good to keep a running set of backups if you can afford the extra storage. Additionally, some apps are able to take advantage of iCloud to back up your files (though whether cloud storage is a viable alternative to hard drive backups is still up for debate). Lifehacker has a good breakdown of software options for backing up your Windows Machine.
What kind of Hard drive is best?
When picking up a hard drive there a few things to consider. First off, you should be careful not to just pick up the cheapest drives you can find to create your backups. Spend a bit more and often you'll get a decent warranty, which of course doesn't cover your files, but gives you a bit of additional reassurance that the drive should last. As long as you're keeping double copies of everything, a warrantied drive will at the very least ensure you always have a new working backup drive.
2.5" drives, 3.5" drives, RPM, and storage options from a few hundred gigabytes, up to a few terabytes (1000 gigabytes) — the specs surrounding hard drives can be confusing. A few points of reference:
RPM Or Revolutions Per Minute; refers to the speed a hard drive can read or write files to disk. Slower drives aren't necessarily a bad thing, especially for backups. A lower RPM drive is a reasonable way to save money when buying drives for long term storage, since you won't be accessing or working with the files as often.
2.5" or 3.5" drives
Hard drives generally come in two sizes: 2.5" or 3.5". Both generally connect with the same kind of connector for power and file transfer, with the main difference being the cost to storage capacity ratio. For backups, 3.5" drives are mostly preferable due to higher storage capacities for the cost.
It's generally assumed that the larger the hard drive capacity the less reliable the drive is. These days you can assume decent reliability up to 3 terabytes, but many would argue it's still better to work with smaller drives (1 or 2 terabytes is pretty standard).
SSD vs. HDD
If you've heard the hype about solid state drives (SSDs) you likely know they're still a very costly alternative to traditional magnetic hard disk drives. Most of the benefits here come with regards to performance. Built with extremely fast flash memory (like the CF or SD card used in your camera), SSD are generally used more as system drives (like in the newest MacBooks). Since we're talking backups, you can safely stick to HDD drives for now, as their track record for reliability and of course larger storage capacity is tried, tested and true.
Formatting for Mac and PC
One more thing to worry about (as if there wasn't enough already) is the system you're setting up a new drive with. By default, Mac and PC formatted drives are not cross compatible (without using third party software). There are of course ways around this, and a bit of research will help you work out a way to access your backup files on both systems.
At the end of the day, nothing is 100% secure
It's a scary thought, but nothing can fully protect you against fire, or theft, or a massive meteor tumbling towards earth. Really all you can do is try to ensure you're keeping an extra copy or two of your most important files stored away (even in a fire proof safe, if you're really concerned).
Whether it's family photos, or a lifetime of work in the digital space, you really can't be too careful. As someone who has faced losing a drive and all the data with it, I can tell you it's not a great feeling, and despite the additional cost of maintaining any of the above solutions, it's worth the additional peace of mind.
(Images: 1. Sean Rioux, all others: as linked above)