Surprisingly to me, I "only" have 57,000 photos and 4,000 videos, all of which take up around 1.5 TB. I thought it was much more than that.
My solution is similar to mollyc's, except instead of a NAS (network attached storage) unit I went with a DAS (direct attached). If you're not familiar with them, NAS and DAS units are boxes that have multiple bays for hard drives. They act like one large drive, but intelligently sort your data across all of the hard drives, and also calculate what's called parity data from which lost parts of files can be regenerated in the event that one hard drive fails. I went with a Drobo 5C (USB-connected, five-bay unit) that gives me a bit over 9 TB of drive space to work with, given my current configuration (four 3 TB drives and one 1.5 TB drive). I can easily expand it by swapping drives out with larger-capacity drives; the unit reportedly can handle up to 64 TB.
There are two main benefits of a NAS or DAS. The first is more professional, which is that your data is always available even in the event of a drive failure. (You can also configure many of these units to continue operating with two drives down, but you'll lose usable space to even more parity data for this benefit.) Recovery is as simple as inserting a replacement drive and allowing the unit to spread the data across the new drive again, a process that slows the unit down but doesn't prevent you from accessing your data. The second benefit is easy expandability. If I snag a nice, much larger hard drive during holiday sales, I'll pull out the 1.5 TB drive and replace it; the Drobo will handle moving the data around on its own, and I won't have to do a thing. It's like having one huge, ever-expanding hard drive.
Even though it's a benefit that a single hard drive failure doesn't take out your data, a NAS or DAS does not represent a backup of your data. It's also still not 100% fail-proof. Failures of NAS or DAS units don't usually result in data loss - usually people can just move the hard drives to a new working one and continue on as if nothing ever happened - but you're still not protected if something catastrophic were to happen, such as if the unit and all of the drives in it suffered an electric surge (haven't heard of it happening but it probably could), or if there were a fire or flood. You could theoretically get a second NAS or DAS and mirror it, but that's a lot of data to be mirroring, and an expensive proposition. Not to mention it still doesn't cover you from physical disasters.
The backup solution I've gone with is an online backup service called Backblaze. They only cover one computer at a time, but they will back up unlimited data from any drives connected to that computer (although I don't think they cover networked drives, so this is only helpful for a DAS, not a NAS). Their pricing is some of the best for these types of services on top of that. The initial backup is long, particularly when you have as much data as I have (beyond my photo/video library), and of course it requires that you have a decent internet connection, but once the initial backup is done it's pretty quick with updated data. They're also a really cool company. If you're interested in hard drives and have read longevity reports on certain makes and models, there's a good chance you've read data from their published reports based on hard drive longevity in their data centers, whether you realized it or not. They raised their prices about a year ago and wrote a really nice message to their users explaining why; nearly every comment I saw written in response was supportive and offered that they could raise it even further and they'd still have loyal customers. It was how I felt, too. Having that offsite backup is wonderful peace of mind, especially when you have a lot of data and all of your data is on a single device. As far as recovery options go, you can do it over the internet, or if you'd need it fast and don't have a fast internet connection, they can load your data onto hard drives and ship them to you. It's nice flexibility.
If you have any questions about NAS/DAS units, Drobo, or Backblaze, I'd be happy to write more about them.