I just made a different post talking about this same thing
Agree that DVD's are the most horrible backup media available. They are easily damaged. Files can easily become unreadable even when the media is not physically damaged. They don't hold much. It's a very poor solution.
External hard drives can have a pretty high failure rate too sadly. What I suggest doing, is getting two HGST (Hitachi) drives, which are by far the most reliable ones out there. Then get a couple of USB3 -> Sata enclosures (something like http://www.amazon.com/dp/B003CJQ69A
). This will give you the most reliable HDD inside of an enclosure that you can easily replace should something happen to it (USB port goes out, power port stops working, very common problem on external drives).
Now that you have this get a program like FreeFileSync. Setup batches to backup all of your relevant data (pictures, videos, important files, documents) to your external drive. One note, recently the installer for FreeFileSync will try and give you bundled crapware. If you're careful with the installer you can choose not to install these, but if your paranoid like me, and you still want the best backup software, you can take a few extra steps. Using a program like 7zip, just unzip the installer EXE. Make your own directory in Program Files, and copy the BIN directory to the location you made for FreeFileSync. Then create a desktop shortcut or whatever for the proper EXE for your system (32bit or 64bit). Free File Sync does take a little time to get perfect, but you can setup batch jobs, and it is hands down the best at what it actually does. I have some complicated backup scenarios, and it has done me great for the last few years.
Now, I said get two drives, that's because if you're out at dinner and your house is robbed, or you house suffers from a catastrophic accident (fire, flood, etc....) then that drive at home as your backup does no good. So get a safe deposit box, they are very reasonably priced (my credit union charges 12 dollars... PER YEAR, for a box big enough to hold HDD, valuable jewely, and important documents). Once every couple of weeks just swap your drive from home with the one at the bank.
Be wary of online services, because for all of these services you are trusting _THEM_ to do the right thing with your data. I've done some contract work with big companies, who offer supposedly very reliable storage, and the truth is, there's a lot of holes in a lot of the providers. Just google "Cloud Provider Loses Data" and you'll see plenty of stories and empirical evidence that cloud storage is not as safe as we think it is. Don't rely on someone else to protect your most valuable data.
I've lost a lot of digital data once, and now I do everything possible to ensure I don't lose it again.
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Richard Maynard