If they're located on your property, then they're protected by 200+ years of case law (in many countries). If not, then you have no protection save the company's privacy policy and willingness to enforce it in the face of government pressure or commercial temptation to sell your data.
There have been too many cases of police and/or security services rolling up at private addresses or small offices, bundling all the hardware they find into a van, and forcing innocent people to spend huge sums on lawyers to have any hope of getting it back.
A box on your desk is not the right answer to this problem.
Some kind of massively redundant disintermediated public data network might be, but we don't really have one of those yet.
If your local server filesystems are encrypted, then it's actually safer from that sort of thing than the file cabinets used to be.
With all of the talking about anonymity, crypto, etc, which are all ephemeral things, one of the strongest things that you have going for you as a US resident is an object inside the perimeter of your home.
The long term point of convergence is that the whole concept of a 'machine' will go away as far as the cloud is concerned. It will still involve machines but you won't know (or care) about how many of them and where they are located.
Something along the lines of Heroku, only then a bit more generic. Computing-by-the-yard, if you wish.