Problem 1: Corrupted System Files - Unable to Load the Operating System
A sudden power outage or system crash can corrupt files that are part of your operating system's essential guts. When these things happen, people who have backups tend to just jump straight to them, but then we're at the time warp problem - if you've already done a week's worth of work since the last backup, that data is lost. Instead, you should first attempt to repair or restore just the system files.
Both Windows and Mac OS X have these capabilities either built in, or on their install discs. Good preparedness doesn't just mean making backups, but also making sure these discs are safe - they can save you some major heartache.
Windows: Corrupt system files happen a bit more frequently in Windows, but it's not difficult to fix most of the time. You should make use of Windows' built-in System Restore, which basically makes daily, miniature backups of your system. It doesn't touch your data - it just backs up system files, so it's absolutely perfect for these sorts of problems. If you're able to boot your PC into Safe Mode (pressing F8 while booting up should do the trick), you can find System Restore in the System Properties settings. If your PC won't boot all the way into Safe Mode, then you'll need your Windows install disc. Booting into that disc will give you the option to use System Restore right on the spot. Since it runs on a daily basis, you can even choose how recent of a snapshot you want (just in case you think the problem started a couple of days before everything stopped working).
Mac: For Mac, it's pretty common that, instead of corrupted files, that you might have broken permissions or other file system issues. You can correct a lot of these sorts of issues by rebooting into Safe Mode (reboot the computer while holding down the Shift key). Booting into Safe Mode will force checking and error correction on the file system, delete cached files, and start the computer in a limited working state that doesn't include anything but the basics. Once fully booted into Safe Mode, you can reboot the computer normally again, and hope that the problem was taken care of in that automated process.
If it wasn't fixed by that, you can use your OS X install disc to run Disk Utility and try to repair the disk. Don't worry, it's automatic, too. Boot into the install disc by inserting it into the drive, and rebooting the computer while holding down the C key (once it starts booting the installation disc you can let go of the key). After it loads and has you choose a language, click on the Installer menu at the top of the screen, and select Disk Utility. Inside Disk Utility, choose the tab for First Aid, find your hard disk in the sidebar and expand it to see the partitions, then select yours (usually named something like "Macintosh HD"). Click the Repair button, and then wait patiently for it to finish. If all goes well, it should give a pleasant report that the disk has been repaired. If, instead, you get a notice about corrupted files, then you can take the final step and restore your system.
Restoring all system files in OS X is actually pretty simple, because you just reinstall the OS. Assuming everything goes alright during the installation (basically, as long as the hard drive's healthy), this will only replace the system files, leaving your personal files untouched and as you left them.
Problem 2: You Can't Log In - Either You Forgot Your Password, or it Got Changed on You
If it's just an issue of a forgotten password that's left you unable to log in (or an unfunny prank by someone who knows what it is), you can reset it pretty easily (and get back to work without hassling with restoring a backup):
Windows: For Windows users, you need to take action prior to losing access to the account (which means you should do it right now). Go to your Control Panel and select "User Accounts and Family Safety", then click on User Accounts. There you'll find the option to create a Password Reset Disk - just follow the instructions and keep it somewhere safe. If you lose access to your account, you can use this to get back in with a brand new password.
Mac: For Mac OS X, boot into the install disc and choose your language, then choose "Reset Password" from the Utilities menu. If that sounds too easy, it's because it probably is - any OS X install disc for the same version installed on the computer will work.
If something more mysterious is going on with your user account, you need a way to get back into your system to try grabbing some of your more recent files, and to investigate what caused the issue. As a safety net, you can keep a separate administrator account on the system, just so you can get back in and check things out. If something malicious caused the lockout, your secondary account should be able to delete the offending files. If not, Windows users can use System Restore, and Mac users can drop in a fresh OS X system install.
Problem 3: Lost Data - Or when You Accidentally Delete Your Life's Work
If you accidentally delete a large chunk of your data - but not anything that affects the OS itself - then a full system restore is definitely an option, but it should be the last one you turn to.
Partial Restore From Backup: If you've taken the time to ensure that your backups are accessible, specifically for instances like this, you can simply grab the now lost data from the most recent backup you made. If your backups are compressed into enormous archives, then they're not exactly quick or easy to work with in a case like this. Making full backups that are basically mirrored copies of your hard drive is far more useful, since you can use them for any amount of restoring that may be needed.
Use a Rescue CD: A rescue CD, like Disk Drill for Mac or Recuva for Windows, can scan your drive for deleted files and restore them if possible. It's usually not a problem if it hasn't been very long since they were deleted.
Save Redundantly: Using a rescue CD has a decent chance of working, but it's easier to preemptively cover the possibly of accidental deletions by saving important files to two different locations (preferably on two different hard drives), or by keeping a daily backup of your most important data. It's not practical in any way to back up your entire system every day, but it's not too much of a hassle to back up a few critical files - like your My Documents folder. If your daily work is seriously important, it'd be best to practice both methods, and invest in a small external hard drive since it can hold both your small daily backups, and also serve as the space to use for double-saving important files.
Cloud Storage: This is when it's also a good idea to have a backup plan for your backup plan. Use cloud storage services like the beloved Dropbox for important files, use a service like Flickr or Picasa Web Albums for your photos (or even store them as regular files in a service like SugarSync.
Keep in mind, of course, that backing up your data is still important. For a little help getting started down that road, take a look at our guide to automated, bulletproof backups - both locally and offsite - with CrashPlan.