What’s wrong with using the cloud? The fact that you need an internet connection, a password to be accepted, to act in accordance with the T&C of your cloud provider, the fact that someone – government, corporation, hacker – could interfere with your data, lose it or just add unwanted stuff to it. Also, if you want to backup your whole system then the various free storage offers are not going to be big enough to do the job, and you’re going to end up paying a lot more than if you backup your system properly.
How about Time Machine? Yes, it’s simple and convenient and pretty much automatic, but its not secure. TM has three major problems. First, it doesn’t allow proper archiving so anything you delete from your HDD will eventually get deleted from TM. Second, it doesn’t tell you what it’s doing before it does it, meaning you are at the mercy of its automated decisions. Third, it’s not bootable. If your whole system crashes or your HDD just fails, Time Machine won’t help you. You’ll have to restore the system or replace the HDD before you can use your machine again.
But there is a much better way, and aside from you providing the hardware (a couple of external hard disks), one that’s also free. The most secure system is to run an hourly or daily scheduled cloner on one disk, and a weekly cloner on the other. You can use SuperDuper or, my own favourite, Carbon Copy Cloner.
If you want to read up on and understand the various backup options and what they entail, you can’t do better than to read this superb post by Apple Discussions member ds store.