Certainly.
I'm a fan of my own Synology device, the DS410 (www.amazon.com), which has capacity to hold 4 disks, and has all of the features I mentioned in the root post. It's a few years old, and has one or two revisions after it, but they were mostly just performance bumps (for which, I've never had performance issues). I also have a friend (who may or may not chime in), who owns (I think) a DS411 or a DS412, and has had similarly enjoyable experiences.
A smaller device, the DS212j (www.amazon.com), has the capacity for 2 disks, but has the exact same software capabilities (as well as the same hardware encryption capability). I believe my dad is running this at home. It won't be able to support a bunch of concurrent access, but that's fairly rare in the instance of a backup device for a home environment.
I'm a bit of a Synology fanboy, as I like their interface, and the relative "hackability" of their platform (to get it to do *exactly* what I want, with the types of programming interfaces that I want), but generally it is extremely friendly to anyone who has operated a web browser before. The devices require a bit of setup (putting in disks, plugging a computer into the device, running its install process, ~30 minutes), but afterwards, it has a number of fun capabilities:
Without a NAS device, potentially, you could set up automatic backups on your desktop machine with a program that writes to a locally connected external hard drive. However, most people I talk to who claim this as their backup solution rarely have their external hooked up as their main computer is a laptop, which doesn't lend itself well to a external HD tether. My theory is: if there is anything manual to get a backup to work, you probably don't have good enough backups.
So, even if you have an external HD you're comfortable with keeping attached, it also means that there is only 1 copy of the backup, and that backup is subject to failure. The way these NAS devices are usually configured is in a "RAID1" configuration, which is an obnoxiously technical way to say "mirrored drives." In this configuration, everything written to one drive is mirrored to the other, allowing for redundancy in your backup disks. If the devices detect something wrong, they can shut off a disk and only use the good one until the bad disk is replaced (without having to be restarted, etc.).
Having the device always be on and be attached to your network, you could always accept backup data (as well as provide other services on the network).
The criticism people have with Synology devices is that they're expensive. ~$400+ for the DS41x, and ~$200 for the DS212, and that doesn't even include the disks (~$200 total for the 2 2TB disks I just ordered). It's expensive for a device that isn't an actively used computer. There are alternatives from QNAP and Bufflo that I've heard good things about, and a few others that probably come up in an Amazon ratings search. What you're paying for with the Synology is its extensive featureset, its interface, and its hardware. When I was doing my research initially, I was finding that some of the more popular devices, though they claimed to be fault-tolerant, were anything but ("You can lose drive A without issue, but not drive B..."). The Synology has no issues with handling faults on single disks, and from what I can tell poking around in the backend, appears to be configured correctly.
Going with a cheaper solution would probably be fine, and it's hard to argue to pay for features you might never use. However, I'm impressed with the output from a small company in Bellevue, and it's not a bad investment to have a good level of confidence that your important stuff is backed up, and backed up reliably.
(Also, I hope you have at least one backup of 10+ years of photos... somewhere... and it's not just on a single hard drive...)
