Not if. When. Hard drives will fail. I’ve had it happen several times. The last time I had a catastrophic hard drive failure was with an iMac. The computer was less than two-years old. The drive failed quickly and absolutely. I had no choice but to replace the drive and restore the machine. As I had been very careful about my backups I was able to restore the machine exactly as I had left it just before the drive failed: all software, all settings, everything. All within a couple of hours.
The approach that I take to backing up is influenced by the device I use and the impact of an unrecoverable computer crash. For me, it means that I must backup my laptop, my office desktop and my studio computer.
Life is made a bit easier for me as I run on Macs. I can use a set-and-forget backup approach to each machine by simply connecting an external firewire hard drive. Time Machine will configure the external drive for full and incremental backups.
I also make sure that each machine has a bootable backup. So, in addition to Time Machine, each machine also runs SuperDuper! SuperDuper! makes a fully bootable backup disk which can complement Time Machine in the event of a catastrophic failure.
If we were to have a fire in our home, I suspect the most important possession I would want to try and save would be our photographs. Memories are very precious and I would hate to lose any pictures from our past. And yet I talk to so many people who have switched to digital photography without any backups whatsoever. I keep copies of all my digital photography on three drives: a primary drive, a backup drive and a RAID archive drive. Each drive keeps the same set of photographs. When I begin to reach the limits of the storage device, I buy three new drives and repeat the archive process. In the event of a fire, it might be possible to grab one of the drives on the way out. Or, it might be better to keep one drive offsite. I have not gone that far as I do keep a subset of my photos on a cloud service as well.
Finally, I make sure that I have all of my software licenses organized. I use a tool called 1Password to manage all of my login credentials as well as all of my software licenses. Whenever I purchase or upgrade software which requires a license to install, I make an entry in 1Password. The 1Passsword data is stored in encrypted form on my Dropbox account. As there is always a copy of the Dropbox folder on each computer I use, the 1Password data is always being backed up.