Center for Data Redundancy:
So you're without backups and you have a hundred gigabytes worth of mess. Where do you start? What would you deem as "most important", and what's irreplacable? After all, even if you have the space or you can get the space, it still takes time to copy it all, wherever it may be on your hard drive.
It can be a bit of an overwhelming process, but no worries. It is possible to keep everything floating around in your digital life safe if you're vigilant. I'll be focusing mostly on local files at first; internet services, both sites that host your content like YouTube, DeviantART, and Blogspot, and sites that host general user data "in the cloud", are too platform-specific to give you instructions in this overview.
(This certainly isn't to say you shouldn't back up your internet-facing data, as sites disappear all the time or make stupid decisions to rebrand and therefore toss your data (MobileMe, anyone?). I'd recommend looking in your account settings for each platform and seeing if there's an export data option lurking, and failing that, seeing if Archive Team has instructions on getting an export going yourself.)
But for now? We look at what you've got knocking around that old, slow hard drive of yours, and why I don't really recommend full install drive backups unless you're really paranoid.
(#) Grades of importance
As far as data goes, some is more important than others, naturally. The best metric is always to ask yourself "how much will it hurt to lose this?". I don't just mean the implications it could have on your life, I mean—will you personally sit there and go "damn, I really wish I still had that" for months and years in the case of a data failure? If yes, you need to save it first.
Data that you can get back fairly easily, things like your game installations from Steam (save games and screenshots are up to you in terms of importance), or movies and major label music you've downloaded or ripped (YouTube videos are an edge case and I'll discuss that later), you're probably good on saving right now. Worry about them later.
(#) Precious: Creative works, photos, personal documents
Your top priority should be any data that's personal to you, that you've spent time on, that no one else is likely to have a copy of. As I'm a creative type, and a lot of the people who read my site also happen to be creative types, this is likely to be your project files and the resulting exports.
This also goes for any personal "life" files, things you keep for your own records and don't have actual print copies of. Financials are a good example of this; Quicken, Excel workbooks, and the like, especially if you're a self-employed business-y type. You definitely don't want any of that getting lost. (I would also recommend print copies, but I'll ramble about that later.)
Emails are also a good idea; if you're using a proper email client (Thunderbird is the prime example, and I'm personally a Claws Mail guy) and not a dodgy, gimped web mail client, you should have the ability to export out email folders and inboxes to a local database file you can retrieve and carry over to another service if need be. You've likely gotten locked out of an email account before, yeah?
(#) Semi-important: Curated media libraries, YouTube backups, and data hoards
Though less so, still important are files and collections you've spent a long time building and getting just the way you like them. These can be rebuilt, though with some or great effort. Backups here are more of the convenience variety, doing work now to save yourself much more in the future.
For me, there is no greater example in this grade than my music library. I don't even have a particularly big one compared to some (just checked, 56GB), but I've been building it for years from a variety of sources (CDs, game rips, Bandcamp, some I've mixed myself) in the highest quality lossless that I care to deal with, if at all possible. I've already lost my library once before, and that featured not only more music, but also hand-formatted lyrics attached to each song. That one sucked to lose.
This is the grade where you can most likely rebuild, but you're gonna hate doing it.
As I mentioned, YouTube backups (and account crawls and data hoards in general) are a unique case. Most of the time, we back up YouTube and other video hosts to keep specific videos that are likely to disappear, like livestreams or contentious content likely to be removed and censored. In the case of some channels that get nuked from orbit, full and even partial channel backups are all we have to go on.
As such, there's still some risk to losing items in this grade. If you're really dedicated to backing up all material from a specific creator, consider your archive top grade. Otherwise, if it's just for a personal, offline archive for ease of access (say, if you have bad internet and you prefer to watch video locally), I wouldn't worry as much.
(#) Ephemeral: Program installs and things unlikely to disappear
And now, we get into the grade of things you likely wouldn't notice gone if they disappeared, or stuff that's so common, you can get it back in 15 minutes.
Program installs are what I think of when I think of this grade. Not only is backing up something as mundane as a web browser install (if it doesn't bury itself in your AppData folder like a ferret in a sock drawer) pointless, in some cases, it means the program won't work correctly when you try to restore from the backup. A clean install, settings notwithstanding, will always feel nicer too.
(Of course, some programs are really that obscure or that annoying to find. Small modding utilities for games are a good example. In some cases, these outright disappear because no one bothered to save them, so if it's obscure enough, back it up. Use your judgement.)
It's this grade that separates a data hoarder from a vigilant backup maintainer. Here's why I don't recommend maintaining backups of every little thing in your Downloads folder: backups are hard enough. My recommended method involves multiple drives and multiple copies of the same data, and even if you have the space, you'll just be making it even more of a process.
This is also why I don't recommend automatic backup solutions that just copy the entire drive's contents to another. More "efficient", yes (I'd say lazier), but it also ignores the need for redundancy, and you should always have multiple copies of your stuff, never trusting it to any one media that is guaranteed to fail at some point. These solutions also require the drive to always be plugged in, thus grinding it down a lot faster, and they save a lot of general detritus you should be regularly cleaning off your drives anyway, like cache and temp files.
Space might be cheap, but it still adds up. Even with me trying to keep my crap intake down, I have about 300GB of space used on my boot partition. Regular 300GB backups would eat my backup drives in a month, perhaps literally thanks to the additional wear of writing to them.
For the average person, backups are simply a way to minimize the pain of a computer releasing the mysterious blue death smoke. For a data hoarder, you're likely obsessed enough to already know what you're saving and why and you don't need me telling you. For you though, internet person who'd just like to keep their stuff? Don't make life harder for yourself. Really think about why you want to keep anything of this grade of data in the first place.
(#) In summation
Think about what you use every day and all the data you generate. Whatever you'd need the most in the case of a personal crisis or whatever you'd miss the most in the case of something failing, that's your top priority. Got a hobby? Self-employed? Save that stuff first. Anything media-related you've poured a ton of time in, be a music library, movie library, or game saves and screenshots, those go next. Anything that falls outside those bounds is up to you.
If you're looking for something to do with your immediate desire to keep your valuables safe, grab a flash drive, some DVD-Rs, a spare computer—whatever you've got lying around, and get to copying that important stuff onto it right now. It's by no means your only step towards keeping your data safe, but doing that alone gives you so much more room to breathe and plan out your next move.
As for building an effective backup strategy, that'll be what the rest of this section is devoted to. I'll be discussing the need for multiple copies of your stuff, different backup media and why you should use everything and trust no one format, the basic 3-2-1 plan to build your backup strategy on, and finally, ways to keep yourself to it. Vigilance is necessary, remember that.