I like the idea that if your computer were to crash, explode, etc., you wouldn't lose all of your important files--rather than being confined to the ticking time bomb that is your computer, these files are floating in a cloud of safeness that hovers above you wherever you go. I also appreciate the comparison of cloud computing to email, because they really do operate under the same principle. I'm with Book Lush, though--I don't really have a huge need for this kind of elaborate file management. Google Docs and Dropbox seem like they'd be more suited for a business than for personal use (especially if you're going to actually be paying for extra storage space--I don't believe in accruing unnecessary monthly obligations--it feels like you're selling yourself into indentured servitude).
When I was first married (two years ago), we didn't have internet nor did we have a printer (nor did we have Microsoft Office, for that matter--which meant I got very good at saving in compatibility mode--except this one time, but my professor was very understanding), and so I would have to save my papers to a flash drive and get to school early enough to go to the computer lab and print out my paper before heading to class (this was most especially tiresome when I had to print out multi-paged handouts for the entire class). So, would Google Docs or Dropbox have been able to make my life easier back then? No, because they require Internet access and I didn't have it at the time. Okay, so the next semester I had internet access but still no printer. I would routinely email my papers to myself and then go print them out at the school. Would Google Docs or Dropbox have been useful for me then? Maybe, but I don't see why they would have been any easier to use then my own email. The email with my essay in it would have been the most recent one in my Inbox, so it's not as though it would've been difficult to find. In Lit classes, we didn't really do group projects (like in Education classes where you do group projects all the time, gag), so the file sharing features of Google Docs wouldn't have been of much use to me in that regard, either.
Here at work, we have our share drive which is pretty awesome. It is incredibly convenient to be able to access my projects from any staff computer. I could see how being on the cloud would be a comparable alternative to being on a server, but it would have its pros and cons: you could access it from any computer rather than being confined to certain computers, but I imagine you'd have to sign in to an account each time you access your area of the cloud, whereas with the server, you just have to be on a member computer. Another drawback is that you wouldn't be able to access the cloud without the internet.
I feel obligated to mention that I have actually used Google Docs' file sharing feature thanks to my sister. Last year, prior to Christmas, she came up with the idea of us all adding our wish lists to the same Google Doc. That way, we could not only see what our family members actually wanted but we could also place a mark in the field indicating that an item had been purchased and this way no one would get an unwanted gift or duplicate gifts. Yay!
I could see using Google Docs (because I already have an account with Google) to save the occasional "important" file rather than simply saving it in my gmail because it would make it easier to find for sure. And if it ever were to come up, I wouldn't have any problem telling a patron about these options.