It's not that hard to combine cloud accessibility with just-in-case offline practicality. Here are a few of the best tools for doing so:
Offline Gmail, Docs, and Calendar apps
Released just before Labor Day for those using the Chrome browser, Gmail's offline "app" is pretty powerful, but more importantly, it's automatic. You install a "Google Mail Offline" app in Chrome, then launch it once to give it permission to start storing your mail offline. Without tweaking any settings or nitpicking labels, the app simply starts running backward in time, letting you know the date to which you can reach back when you're offline. You can write and reply to emails for later sending, archive and label messages, and generally work your inbox how you normally would, just without new messages (and that can be really nice). You can also keep multiple accounts offline, simply by signing into them as you normally would, then launching the offline app.
With that app installed in Chrome, Google Calendar and Docs can also get some offline powers. Head to your Google Docs or Calendar app, click the gear-like icon in the upper-right corner, and choose the "Offline" option for each. At the moment, these offline tools are much more restricted than Gmail: You can't create new documents or appointments, the Calendar archive only goes back to June 2010, and the Docs list doesn't include presentations or PDFs you may have uploaded. Still, like Gmail, these apps are automatically fed with material while you're online, so when you suddenly find yourself disconnected, you'll have a good bit of what you need on hand.
Keep using Microsoft Office with a Google Docs backup plan
Even Google can't pretend that for some projects, workers need access to more robust Office tools than Google Docs can provide. That's why Google offers its own Cloud Connect, which forms a bridge between Microsoft Office on your Windows desktop and Google Docs. You don't get the as-you-type collaboration with another person, but every time you save, your changes are pushed to anyone else who has the document open. It's entirely free from Google, and works with Google Apps just fine.
Then there's OffiSync, a third-party tool that offers the same core Office-to-Google linkup, but with some added features. OffiSync's plug-in provides a more real-time collaboration view, and having Google Image Search right inside PowerPoint is pretty handy--as is having an extra copy of your document saved, in its native .doc /.xls /.ppt format, on Google's servers. OffiSync's free version covers quite a lot of its features, and the paid version is fairly cheap at $12 per year, less for group licenses.
A more automated Dropbox
On its own, Dropbox is a pretty wonderful thing, and a great tool for keeping files accessible on any computer or smartphone you have, as well as on the web. But to make its tool easy to use, Dropbox uses a true "box" model--a certain folder that syncs up everything in it. If you're the type who keeps files on their Desktop, or in particular folders, you're somewhat out of luck.
But if you don't mind pulling a quick, tricky maneuver, you can get Dropbox to sync nearly any folder on your system and watch it constantly for changes. Mac users can use a utility called MacDropAny, and Windows users have DropboxFolderSync. Both allow you to simply choose a folder to add to Dropbox's constant backup vigilance. If those don't work for you, or you're on a Linux system, you can try a command trick outlined at Lifehacker.
Now you're covered both ways--able to get at your files and work documents from nearly any browser on any computer, but also secure in knowing that you can get by without the web from your hard drive. At least until you go crazy from YouTube withdrawal.