While you both are quite correct (local backup to external hard drive(s) is a terrific and simple idea), it ignores one BIG factor in protecting your data.
Power.
During my 25 years in the computer industry, the single most common factor in damage to computers/peripherals is power: “dirty” power (slap a meter to your household current sometime and see just how “clean” it is; you’ll see spikes that will shock you); power surges, etc. If such can severely damage or destroy your computer/hard drive(s), it’s a pretty safe bet that your external drives are subject to the same thing and are also at risk.
Off-site backup a la Carbonite is NOT a bad idea at all; it virtually eliminates this risk.
IF you can afford it, I’ll add another recommendation to you all; something I did at my own house. I paid an electrician a few hundred bucks to run, install a few dedicated 20A (20 amp) lines specifically for some heavy-duty computer gear. While I was at it, had him do the same in the family room so that the home theater components are also plugged into such a dedicated 20A line.
This was a very good move. No refrigerators, freezers, etc. etc. sharing those circuits; these lines are totally “dedicated”, dramatically minimizing the opportunity for any serious electrical damage to the computer components. Additionally, I HIGHLY recommend a heavy-duty uninterruptible power supply (UPS)/power conditioner. I got a killer one, brand-spankin’ new, on eBay for a relative song. It, in turn, is plugged into a dedicated 20A line; have had zero power problems.
One final recommendation: Check your renter’s/homeowner’s insurance policy and make sure your electronics, especially computers, are covered in case of power surge/lightning strike. It’s cheap coverage; please GET it. It won’t protect your data (hence the discussion above), but it will help you in replacing expensive gear if necessary.
Hope this helps.
I have a whole house surge protector and all of my sensitive electronics are on APC UPSs.