Ya know, if there's only simple storage, I use my email from my ISP. (not the mainline freebies like yahoo or hotmail type that gets hacked, however). Since we all probably pay for internet, your ISP will provide you with a certain number of email accounts anyway. Ours lets you have up to 4.
To store, just email yourself with the attachment document you want to save, and create a special folder to move that to using their web based version of email (as opposed to a local client). Your stuff is then accessible from any computer in the (hopefully unlikely) event your house burns to the ground or something you have your computer records. Most give you several gigs these days, enough for all office types of documents, small programs, zip files, important pictures and whatnot.
If you have a huge amount of pictures or videos, you can buy removable media and store it in a safe place. I never got into keeping videos because even today the techhnology is not there yet to store a lot of videos like in the analogue days due to the many, many gigabytes it uses. In that case, it would probably be better to attach an additional removable disk, but unless it's solid state media, you'll have the same problem with an attached drive eventually. Fortunately, I think most is going solid state these days, and I can't wait for the day that all computers will be that way without mechanical drives.