I've lived through enough power outages to know there is no substitute for a legacy corded analog telephone that needs no electricity.
I love my cellphone, but the underlying system can fail due to wind, the loss of power or even just volume, as the East Coast experienced with the earthquake just days ago. Cordless phones are great too, but I will always have at least one (if not two) telephones that don't require electricity.
If you depend on computers, you probably have them connected to a surge protector. If not, start taking advice from different sources.
Personally, I'm way too pessimistic for mere surge protectors, I depend on a UPS (multiple actually). Nothing to do with brown trucks, a UPS is a big battery that powers a computer when the electricity fails. Good UPSs do much more than that, but that's another topic.
Should you lose power, the battery in a UPS can be put to other uses such as powering a lamp, running a radio or recharging a cellphone. Think of it as a poor man's generator.
It's also possible that a UPS can provide Internet access by powering a broadband modem. I haven't yet tested this, and hope not to get the chance.
Hurricanes, of course, scream off-site backup, but a large storm like Irene begs the question of where, geographically, your off-site files reside. Someone on the east coast is better off storing files on the west coast of the US rather than the east. And, since data centers can fail, its best for off-site backups to reside in more than one physical location.
Put another way: It's a hurricane. Do you know where your backup files are?
A quick review of Dropbox's website failed to turn up any information about the physical location of the data center they use, let alone whether they have multiple locations. All I could determine was that they use Amazon S3. My guess is that if they employed multiple redundant data centers they would brag about it.
Rsync.net takes the opposite approach, they are very up-front about where they store your data and whether they keep one or more copies. Simply put, if they keep one copy it costs less than if they keep two copies. Fair enough.
And, when you sign up for the service, they let you chose the physical location for your off-site backups. In the US, they use data centers in San Diego and Denver, both well out of the reach of Hurricane Irene. Outside the US, they let you store files in Zurich or Hong Kong.
Websites too, may need a backup.
If your main website is, for example, mycompany.com then it costs little to have mycompany.net or mycompany.org as a backup. So as not to put too many eggs in one basket, you could register the backup domain with a different registrar from the one that registered the main site. Likewise, host the backup website with a different hosting provider, preferably thousands of miles away from main site. With a low end hosting account, you can have a backup website at the ready for under $100/year.
Finally, if the power does go out, it's best to unplug the computers. When power is restored, it may come back with a surge and there is no reason to test the limits of your surge protectors.
Update August 29, 2011: Wouldn't you know it. Two days after writing this, I heard about someone I know (call them Person X) who, using their computer, works at home on Long Island.
Person X's house lost power due to Hurricane Irene. Person X's parents house was completely flooded. Person X's mother-in-law's house on Long Island was also flooded. Person X does not have a land line and, no surprise, their cellphone eventually ran out of power. Person X works for a small company, they're not being available was a big deal to the company.