Use SugarSync to back up your files. You get 5 GB of space free and you can sync between computers/devices and share with others. If you use the link above, you get 5.5 GB and I get an extra 0.5 GB, too.
This is as far as most people need to read. The rest is for special situations and background.
Small businesses and non-profits can also benefit from SugarSync. Create a work account and share your folders with coworkers. They can either just view the shared folders online or sync to their own computers. You can enable them to edit, add, and delete files or just to view. Each folder only counts toward one user's 5-GB limit.
For large numbers of pictures, use Google's Picasa Web Albums. You can download Picasa to run on your computer or just use the online version. Google gives you 1 GB of free space, but doesn't count pictures and videos under certain sizes. Plus, you can purchase 20 GB more space for $5 per year. That's PER YEAR, not per month. That's cheap enough even for me. Be sure to set Picasa to sync your photos at their full original sizes. NOTE: as of 7/3/2011 Picasa is in flux. Those who sign up for Google+ will find privacy policies changing to something more like Facebook. You've been warned.
You can now download your Facebook activity directly on Facebook. To back up your Facebook and Twitter activity automatically, use Backupify. It's still a bit primitive, but by the time you want the data it may not be so primitive anymore. You get 2 GB of storage for free.
If you have a WordPress website, I recommend the WordPress Backup to Dropbox plugin. Dropbox gives you 2 GB free, or 2.25 if you use this referral link. It backs up the database and files automatically for free. What more do you want?
You know you need to back up your data. Computers don't live forever and nature is not kind to data. Now there are tons of free and cheap and easy solutions, and I've written this wonderful post, so you have no more excuses.
My research started a couple of weeks ago when my hard drive started making a noise. An unhappy noise. I googled it, and no one offered any hope. Bad noises are just a warning that your hard drive is likely to fail. I looked up all the info I'll need to replace it if it does crash. And then I decided I wanted more stuff backed up.
I had been using Mozy and Windows Live SkyDrive, but I wanted to back up more pictures and some weird file types and I wanted it to be easy (after the research part, which I do also for you). Easy means that I need sync – the service should keep track of any changes in the files and update them at least to the online service and maybe to other computers like my husband's or my smartphone I'm going to have one day.
Windows Live SkyDrive gives 25 GB of free space, 5 of which can be used for Windows Live Mesh, which does sync. But, both will only take certain types of files. In particular, they won't take Outlook .pst files! And if you use Outlook, you should definitely be backing that up. I'm not even using Outlook now, but I have a backup file from an old account I want to keep. And outside of Mesh, SkyDrive doesn't let you upload folders, just file. And the final nail in the coffin was that Windows XP is not supported, so I couldn't download Windows Live Mesh to my husband's computer. Sheesh, Microsoft, just support your own products!
Mozy is a great service and I recommend it except that SugarSync is better and bigger. Mozy Home gives you 2 GB for free, or 2.25 GB if you use my referral link.
Dropbox is the same basic deal as Mozy. See above for use backing up WordPress.
It's great that Facebook now lets you upload pictures at full size and download a backup of all your data. However, how often will you remember to download that info? And basically I don't trust Facebook to keep stuff. Facebook and Twitter have always been about showing what's happening now, not about storing that stuff for later. Maybe Facebook will change my mind in time.