For example KIMDOTCOM and the idea of an encryption key.
Just looking to get my brain going...
For instance, I worked at a place that used Google docs for everything and I hated it. I couldn't make presentations in anywhere near the quality I could make with Powerpoint and this made it harder for me to maintain the professional image I wanted to maintain.
Similarly, people are so trained to use Google, Gmail and such that we've all given up on having desktop or small office search or having a local mail client which is workable at all. With email dominated by zombie products like Gmail and Outlook, it's no wonder that it's 2013 and we still get forged mail from visa.com.
The funniest one is that Duck Duck Go is trying to distinguish itself from Google and Bing by not having personalization, but on the other hand, Google and Bing do not have any real personalization. They do some simple parlor tricks that confuse SEOs without hurting the rankings, but they are stuck with P@1 at .70 by the fact that neither one can or will (because of business model, expense, laws in the EU, not knowing how to evaluate personalized search results, etc.) deliver a system that uses a user model to make the system more useful to the user.
There could be a real role for a system that lets you have your own "intelligent agent" that works for you and could do things that can't be done by companies that are trying to sell you as a product. Such an agent will be an enemy of the "API economy" but so what...
If you really want to innovate in the Cloud Computing industry, take your time to figure out a useful problem to fix. It might help to not think about Cloud Computing itself.
One could almost read your wording to have said, "...opportunities for start-ups to do something that the likes of DropBox, Google Drive, SkyDrive, ect wouldn't allow you do and likely won't ever allow you to do." The problems of going against these behemoths is that no company will trust you over them, which means you'll have to fight for B2C. Which is fine, except that Google and the others are marketing the crap out of that to their email customers all day long. That's the 'wrong row to hoe' as they say.
So back to the "interpretation" of what you said - the only opportunities that I can see are serving content that the big guys won't touch: porn, piracy, encryption, etc. But that puts you square in the middle of two groups: aggressive law enforcement types and "unethical" groups of others. That's just not a place I'd want to be.