The most important thing about backing up important files is that you do it yourself, fairly often and redundantly in different media. That way, over time, you'll have opportunities to rescue data that is important to you, and then you'll have practical experience.
I have been doing this for about 20 years. I have used everything from magtape to 8 inch floppies, to zip and jaz drives, to cds, dvds, memory sticks, external hard drives and USB devices. I've used RAID NAS, and a couple generations of cloud services.
The most important thing I've learned is that when it comes right down to it the things you value most, you probably don't even have digital copies.
So I went through this exercise a long time ago (1989) when there was a fire two doors down from my apartment. I had already done the drill so I already had prioritized what I was prepared to lose in a fire, and what I could not bear to lose. My priority was my written diary and personal photos. I had it all in four milk crates and was ready to evacuate in under 10 minutes. Everything else, books, records, cds, clothes - were all replaceable.
Rule #1 Go through all of your stuff and see what's irreplaceable.
Pretend you have a $1,000,000 fire insurance policy and your house burns down. OK. Whatever you can buy a better new version of is basically disposable. Actually, insurance companies (and police departments) would like you to go through this very exercise. If you have lived through a home burglary or fire, you'll know this. Everybody should know exactly where that irreplaceable stuff is. My dad's college beer steins. My silver framed wedding picture. My autographed bass guitar. The cuff links from my wedding.
Next, you would think official documents and stuff would be pretty valuable, but in fact it's mostly sentimental. Tax returns, death certificates, citizenship papers, passports, birth certificates, check stubs, medical receipts, degree certificates. All on record somewhere else. Disposable. Inconvenient if you don't have them, but really... that's only because you're in a hurry and you didn't plan. Admit it. And I have to say, if I had been divorced, or lost custody of my kids, those papers I probably wouldn't want around.
The big pain in the neck is scanning your important personal papers. Just do it. Once you've done it, print them out again and store them in boxes. Now you have originals, digital copies and physical copies. Store the physical copies at a relative's house. If you don't have any relatives, rent a big safe deposit box at a bank (preferably a bank downtown) and put the most personally valuable ones in their vault.
Now with your digital copies, buy an external hard drive and dump them all over into them. Next buy a premium account with Evernote and send them all into Evernote. Obviously you want to use PDF. It's probably the most robust digital version of anything, although JPG is pretty damned good as well. Next backup your spinning hard drive with Backblaze or Carbonite. Finally put the most important, important sentimental docs also into Dropbox and Amazon S3.
That's for documents. Next for pictures.
It shouldn't take long to scan all of your prints. If you have color slides, they are the most troublesome. If you have super 8 or 16mm film, Kodak has an (expensive) processed to digitize all that. I would also search around for a local camera shop that converts Hi8 and VCR tapes to DVD. That's expensive but worth it. Movies of your kids are priceless, no matter how insipid the action.
I've converted thousands of my own and my father's photographs. I have to say that unless they are 8x10 or larger prints, then once they are scanned, that's the best format. So don't bother getting reprints, you'll enjoy them more online anyway. For those exceptions, there is Shutterfly (I think). Remember redundancy. Make your favorite pictures gifts to other folks. We make picture calendars and Christmas pictures every year and send them to friends and family. Funny how those show up 15 years later. Right now Flickr is the best service for my money. Google + screwed up what was wonderful about Picasa, and Amazon is coming up with a new service. Apple photostream is a brilliant idea, well-executed, but that's just 1000 pix.
Rule #2: Prioritize what is irreplaceable.
It will turn out that 'all of your digital stuff' will fall into the area that Taleb calls 'Mediocristan'. Basically there will be a predictable bell curve distribution for the number of digital assets you will find irreplaceable. For example, if you pick your favorite movies, chances are you'll have anywhere from 50 to 200. But you are very unlikely to have 2000 favorite movies. Similarly you are very unlikely to have 20,000 favorite songs or 10,000 favorite pictures. Your entire library might be that big, but not your favorite, irreplaceable ones.
The good news is that your favorite movies and songs are probably going to be other people's favorites as well. So movies and songs are likely to be disposable. So is software, except for the stuff you've written yourself.
All that said, I've got some 50,000 photos all over the place redundantly, but about 2300 that I keep redundantly in Dropbox, Flickr, on DVD, on USB sticks and in S3. All of them are synched to my phone, and some fraction of them I've posted to Facebook and in my blog. I have it covered.
Rule #3: Be Redundantly Redundant.
If you don't eat a Big Mac, you'll forget what a Big Mac tastes like. But you probably won't because there's a McDonalds everywhere. You should periodically visit your favorite digital assets just to make sure you can. I like looking at my resumes from college and pictures of my wife 30 pounds ago. I like listening to Beethoven's Moonlight Sonata and I could watch the Fifth Element another hundred times. (Multipass!) There's no point in stuff being digital unless you checkup on it. Go eyeball those CDs you burned 10 years ago. Mount that old Porsche Design 150MB hard drive. See what's on that old memory stick.
Rule #4: Review and Recycle.
Put old media into new media. Put new media into old media. Look at those old Grand Canyon pictures, are they really so precious. Your priorities change. You *should* overspend on your redundancy until you get to the point where you know you have too many copies of that one song and it's costing you too much money to store it. Then you reprioritize again. See if there's a better storage deal out there.
Rule #5: Plan for the Disaster.
After the disaster happens, are you really going to care about all that stuff? Maybe you could admit that somebody else has a better collection than you? Have you really had a garage sale forced on you because you were desperate for money? Then you know that #3 wood you used to hole the Par 3 at the municipal course is actually only worth about $20 bucks.
I learned these lessons because every year without fail for about five years straight, one or more of my hard drives would fail. I got really good at using recovery utilities to get data out, which is why I have thousands of songs titled like Recovered_00493.mp3. And oh by the way, the open source MP3 guys were right all along. So remember that the open source stuff lasts longer. And also do NOT waste your money on anybody's NAS. If you think RAID5 will save your bacon, think again. (Up your's Iomega!). Just check around for what people charge for recovering hard drives. It's highway robbery.
Rule #6: Do it yourself, plus the Rich get Richer.
The best kind of redundancy is the kind where you can depend on other people's self interests being aligned with your own. Find the big dog market leaders and place bets on their technology, but be smart about it. Pay attention to where other people are placing their bets. Amazon right now is a sure thing, and over the past 3 years have kicked Apple's ass when it comes to storing your music. But not long ago Apple's iMatch was boss. Flickr is great for pictures, but pro photogs like other services. Don't follow the crowds, follow the pros, but keep doing it your own way too. A little paranoia goes a long way when it comes to disaster planning. It might even change the way you look at everything.
Rule #7: Expect Failure, and get over yourself.
If everything you did were so precious, people would line up to do this crap for you. Ask Bruce Willis if he has enough pictures of himself and his ex-wife. I know right? Every system fails. This is all about cost/benefit analysis. But in the end, we all die, and your surviving ex-wife is going to do things in your house that would set your teeth on edge. So recognize it's all small stuff, except for this chair.