1) It's not known if computer security is even possible in theory.
2) Even if computer security turns out to be possible, then implementing it correctly is still a difficult problem.
3) Even if computer security is possible, and someone manages to implement it correctly, you have no idea if they're lying unless you have full access to all parts of the code and environment.
4) Even if computer security is possible, and someone manages to implement it correctly, and this can be verified, then you sure as hell shouldn't give them any stuff you care about, because they'll put in in a system that's theoretically sound, verified, correct and proven to be able to stop you ever getting it back. In short, you'd be fucked.
Whilst all software fails the first test, and most software fails the second test, Dropbox also fails the third and fourth. Don't use it, or anything like it, for anything private. If you still want to upload stuff then there are plenty of Free Software programs for doing so, ie. they pass tests 3 and 4.
Yes, I know that banks, credit card companies and the like send transactions over the Internet, but that doesn't mean that doing so is secure. It means that doing so is cheap. So cheap, in fact, that they can afford to pay for insurance to cover all of the fraud that happens on the system every day.
Update: DropBox are now being investigated for false advertising. What's the false claim they made? That they're secure. Specifically, DropBox claimed that their employees cannot access any of the data stored in their system, which turns out to be complete bollocks. The investigation is being made since DropBox has provided a simple, quick, insecure system but presented it as a simple, quick, secure system; whilst companies attempting to create real secure systems, which inevitably end up less simple and quick than DropBox, have been left in the dust by DropBox.
The moral of the story is to run your own clustered filesystem, or if speed isn't your main concern then use FreeNet.