I keep my machines other than the one I freep from isolated from the internet as much as possible.
I absolutely never rely on the internet for long term storage.
The beauty of Dropbox is that you don't have to. Yes, there's a copy stored on their servers, but it's best utility is to synchronize files between multiple computers. I have three computers running Dropbox, and (unless they're disconnected from the network), I can add/modify files on one of the machines and see the changes on the other ones.
The network storage is, to me, simply a side effect.
One thing I haven't tried yet, but is a feature, is sharing a folder within my Dropbox folder with other (specified) users for a collaborative project.