What I would recommend for flash-based storage is something like this
(the latter of which requires absolutely no wires or ribbon cables, but requires to be inserted vertically, taking up space). There’s also these
and I'm sure others. This sort of hardware is common among hobbyists/small-form-factor people.
In terms of other things, most modern motherboards come with tons of extra headers (including USB2) that require no wires travelling from outside in. For example, one of my friends (a very bright one) built his own MythTV HTPC (including designing the case) with his own homebrew infrared receiver. The receiver required a serial port, but instead of using the external one (with the receiver sitting outside, on top of the box, he connected it to a serial port header, and nicely fit it inside his case.