Private DIY Solutions
One solution that is particularly attractive is to write (or burn) your data onto writable DVD’s known as DVD-R’s. This requires discipline on your part to do this regularly and you always have the risk of some of your data being unprotected. When I was going this route I would not delete the pictures from my camera until I have them on my computer hard drive and burned them to DVD-R. I would then take the disc into my work and leave it in my desk drawer to protect against something taking out my house. I know someone who had a fire and their backups were right next to the computer, fortunately the fireman pulled the computer and discs out of the house as one of the first things he did, otherwise years of photos could have been lost.
Another option is to buy an external drive and plug it into your computer, backup your data and then unplug the drive. You also need to physically protect the drive by moving it to a different location or putting it into some kind of fireproof storage. You can also buy external drive that are in a fireproof case. I have never had one of these so I cannot comment beyond that fact that they exist and if I was running a business I would buy one for my business data.
Personal Cloud/Network Attached Storage (NAS)
Something that is a little more convenient than an external drive is storage that you plug into your home network and it just sits out there providing storage. There are several build your own solutions (personally I use unRAID) and there are out of the box solutions by Western Digital, Netgear, Synology and Apple has a unit for MAC users. Just search someplace like Amazon for NAS. It is important to note that this does not solve the problem of physical damage to the unit as it is typically in the same place as the computer with the data you are trying to protect.
While you may have heard of BitTorrent in connection with illegal sharing of things like music and movies, it is at its heart something called a peer-to-peer protocol. This means that there is no central server that you are connecting to that has the data and controls things. What it means for you is you can set up your own private peer-to-peer network and share data automatically and this network is completely secure and private. This is free for personal users and can be downloaded here. However it does require a bit of computer skills on your part to set it up. The best method would be to find someone you trust and set it up so they get a copy of your data and you get a copy of theirs. Or you can put your own computer or NAS unit at their place just to serve as an off-site storage locker. Further if you have a second place of your own that has an internet connection you can set it up there. For those with more technical skills you can do this with a $35 Raspberry Pi and a hard drive big enough for your data. Additionally if you have family members who you know will not take care of backing up their data themselves you can use BitTorrent Sync to automatically have a copy of their data on your system. If you are not going with an automatic online solution, this is what I recommend. Actually I recommend you do both just to be sure.
Any of these hard drive based storage solutions will likely mean you are copying large numbers of files that can also be large in size. Whenever you are copying or more importantly moving files from one drive to another it is important to validate that the file did not get corrupted during the transfer. Windows for some reason is slow in doing large copy jobs so I use a program called TeraCopy (http://www.codesector.com/teracopy). TeraCopy also have the option to validate the file after copying so that you know your backup copy is good.
USB Thumb/Flash Drives
While these are incredibly convenient for transferring files from one device to another or to just have some storage in your pocket these should be viewed as a file transport solution not as a backup solution. There are technical reasons behind this that I won’t go into but I have had too many of them get corrupted by moving them between machines to rely on it as a backup. Generally a format will “fix” the problem, but that also means all your data is gone. Don’t rely on this type of drive as a backup or more importantly the only place you store important files. You have been warned!