While I am sure there are all kinds of scammers looking to score after any hurricane, apparently some of these people knocking on your door might be legit. It seems the FEMA workers generally travel in pairs, and a Red Cross rep said she would sometimes go with them, as well. Basically, if the person at your door is alone, it seems less believable.
I'd also ask for ID and check credentials. It's not like they can really process your claim right on the spot, so you can probably get the information and fill out forms online or send to an official address. If you're looking to get free fixes for problems completely unrelated to the hurricane, then you probably deserve to get scammed, but I'm sure that never happens around here.
While it might seem odd for government officials to canvass neighborhoods looking to give away money, I guess it must the result of some kind of need. To me, it seems more efficient to send out some kind of notice with an official correspondence, like taxes. It just seems like paying people to walk through our sprawling neighborhoods isn't the best use of FEMA money.
After looking into it further, I think that it has something to do with special needs and people who can't figure out how to fill out the forms. You might assume that anyone with the wherewithal to own a property should be able to figure out how to fill out a FEMA relief form, but you might be wrong. There's also a chance that coming out to see damage might allow FEMA to assess early in the process, so that someone claiming all kinds of damage that was obviously a result of improper maintenance can be advised to drop the claim before more people have to get involved. There's also a chance that FEMA going door to door will stop scammers trying to do the same thing.