Personally, I don't trust the folks at Dropbox much more than I trust a random hacker. (No offense, of course. I just don't know them.) It's not even a matter of a security breach. Can you really be sure that one of their interns can't gain access?
By that logic, you should also not trust the guy who makes your next carry out. You don't know him after all. For all you know he could be some evil guy who likes to spit in the customers' orders.
If you've ever worked in a kitchen, you'd know that you definitely shouldn't trust that your food isn't spit in. It doesn't happen often, but it happens. Luckily, occasionally eating some spit isn't that big of a deal, and it's something I accept as part of the the convenience of having food prepared for me.
On the other hand, if you had very sensitive financial or business info on Dropbox, then the consequences are much much more akin to having your food poisoned. So then you're question becomes: why aren't I afraid of being poisoned by my take out? And the answer is that (1) nobody stands to gain from me being poisoned while they do stand to gain from stealing my financial info, and (2) the perceived seriousness of poisoning means that many more resources are put into finding and punishing people who poison (per incident) than people who steal financial data, so people are strongly discouraged from the former.
By that logic, you should also not trust the guy who makes your next carry out. You don't know him after all. For all you know he could be some evil guy who likes to spit in the customers' orders.