One of the most interesting messages Google tries to get across in its Chromebook campaign is the idea that the hardware is disposable. If your Chromebook falls into a volcano or gets run over or stolen, you're out the cost of the hardware, but that's it. You don't lose any data, and the crook/volcano god doesn't get access to it either. All you have to do is grab a new Chromebook (or any PC that can run the Chrome browser) log in, and you're back in business.
Most of us can't use a Chromebook full-time. We use programs that don't yet run in a web browser, we play games that require local asset files and don't sync to the cloud, and we have a lot of data we need to hold onto--more than will fit onto a few lousy gigabytes of local storage. But we can take a page from the Chromebook, as it were, and make our data resilient and flexible--resilient, so a hardware loss doesn't mean data loss, and flexible, so that we can pick up pretty much any computer with an Internet connection and be able to work. After all, if you lose your Chromebook, you don't need to find another Chromebook to access your data; you just need to log in to your Google Account from anywhere.
In order to get Chromebook-level data security on our "real" computers, we need two things: good backup software, and good syncing software. All of your data deserves to be backed up, but not all of it needs to be immediately accessible. With a good backup, your data is safe, and with a good sync setup, you can have near-instant access to whatever subset of that data you deem worthy. The good news is that this is now really easy.
I'm not just idly pontificating; I just did some spring cleaning, including a clean Windows install on my desktop, and this is how I prepared, backed up, and synced my data.
Note that this guide is written from the perspective of a Windows user, but the main points are valid for Linux and Mac OS X users as well.