The asker explicitly excludes cloud solutions. It's depressing that people have recommended various cloud solutions nonetheless. Apart from not being answers to the question, these solutions are totally awful for large quantities of data. Amazon S3 may be nearly free if you want to store a few gigabytes, but if you want to store a few terabytes you are going to pay through the nose, and all the other service providers are the same. 2Tb would cost $234 per month just for storage, transfer cost not included. For the price of two weeks of S3 storage you can buy a 2Tb external disk. For the price of upload, download and a month's storage, you can buy four or five such disks and have as much redundancy as any normal person could ever need.
What will be depressing is when you loose all of your stuff. It will happen. I wouldn't want to suggest paying a hosting service for risk of depressing you further. So I will leave everyone else with this story.
Last week someone I know watched the house across the street burn down. According to the story the fire started at 3am with a lightning strike. There was a big hole blown in the roof by the strike. My friend tells me that the couple had time to get out with the dog. They lost everything but their lives.
If they had put up their important files, photos etc on a hosted site they could get back on their feet much more quickly.
In the past I have spent thousands on everything from a full blown Netfinity server with raid5 to a big pile of 3.5" disks. Sure you can get a 1TB USB drive, back up your stuff and put it in the fire safe. But it is expensive in time, hardware, and electricity.
I pay (insert company) $20 bucks a year to host my important stuff, use (a different company) for nightly automated backups, and the rest in on the local hard drive. I am not recommending any particular solution. If you don't have an off site backup that is current you might as well not bother.