You can even use Time Machine to back up to remote network drives (say, drives connected to your Airport base station).
Of course, Time Machine requires that you buy that hard drive, and that you connect to it regularly. There's another option that requires no special hardware on your end--only a monthly (or yearly) fee, and an Internet connection:
Extra safety option: CrashPlan
CrashPlan isn't the only online backup solution out there, but it's consistently a favorite among the Macworld staff. For as little as $3 per month, you can back up a single computer; for as little as $6 a month, you can back up as many as ten of your family's computers. (Those prices require paying for four years of service upfront; paying monthly incurs a a higher per-month fee.)
With CrashPlan, you needn't worry about buying (or replacing) external hard drives, and obviously you don't need to worry about connecting one either. As with all online backup services, CrashPlan works by backing up your files over the Internet. And since CrashPlan backs up your data on its own system, you avoid the single-point-of-failure situation that a single Time Machine backup drive creates.
You sign up for CrashPlan, pick out a plan, download the CrashPlan software--and then wait. It automatically backs up your Mac over the Internet to CrashPlan's servers. You can launch the app and watch its progress, or just leave it closed and it will silently do its thing.
Out of sight needn't be out mind: CrashPlan can email you or message you via Twitter with status updates on your backups--along with warnings when a computer hasn't backed up in a few days. When you need to restore a file, you can do so via the CrashPlan app or the website. Like Time Machine, CrashPlan even backs up multiple versions versions of your files, meaning you can get at earlier copies of a document if need be. And it holds onto files you delete, too. The service offers impressive peace of mind for the price.
Don't worry about bootable backups
None of these options--Dropbox, Time Machine, or CrashPlan--offers a means of creating a bootable backup. That is, you can't start up your Mac with any of these options if your main hard drive fails. But that's okay now, thanks to Lion's Recovery Mode.
If you're running Snow Leopard, or if you aren't comfortable with Recovery Mode, you probably want to start making a bootable backup as well; the most popular tools for doing so are SuperDuper and Carbon Copy Cloner. But those require a smidgen more care and attention, and we want to ensure you keep your New Year's resolution, so let's not sweat those options this time around.
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