Chris Gillmer asks the same question on Web Worker Daily in a post titled "The Downfalls of Online Applications". He points out that you need to consider what happens not just when the lights go out but also if/when the company providing the service closes down, is bought out or disappears down a sinkhole? Less dramatically, what happens if that service is hit by a denial of service attack or some other connectivity interruption?
Before you start shutting down your online accounts and moving across to paper systems, consider that these sorts of eventualities should be managed just as you would any data service. Back your data up somewhere accessible. As you may have gathered, I use Google Calendar for some of my calendars. To protect against this sort of problem, I subscribe to those calendars using iCal which is, in turn, synchronised with both my iPod and my mobile phone. That pretty much takes care of my diaries and tasks. My address book is backed up to Plaxo and there are current copies on my mobile phone, iPod and Address Book. If Gmail enabled a way to import all my contacts from Address Book (or, better yet, the ability to synchronise my contacts), I’d do that too. You can do similar things with all your data and use a combination of a local and online service to keep multiple copies of your data.
The point is there are simple ways to plan for most interruptions and ensure some degree of continuity. The thing is to actually give it some thought and do what you need to do.