The technical term, used (we suspect) to either scare off non-geeks or to sound intellectual is isomorphism. (What do you want to bet we'll one day hear the term in a science fiction show: "he's gone isomorphic, Jim"). Another name is self-transposing system.
We prefer the term consistent-interval, or simply consistent, as in consistent keyboard. In such it turns out that, by design, every musical interval, for example a major third, always travels makes the same angle and distance. Further It turns out that any consistent keyboard system always makes the same shape, a triangle, when you make a 3-note chord. This is easy both on the fingers and on the ear.
For starters, here's the rather technical Wikipedia entry: Isomorphic_keyboard
Brett Park, on his Shiverware website, offers the chance to try out any isomorphic keyboard in a simple program that runs on the iPad et al.
He has studied the designs a fair bit, and has these pocket summaries, reproduced here with permission:
Jim Plamondon has a succinct and easy to read analysis, but it does not detail the implications: Jim Plamondon on Isomorphic keyboards
Brian Hayden, who (re-)invented the isomorphic concept, and especially the Kaspar Wicki/Brian Hayden key layout did a deeper evaluation of isomorphic keyboards, which has been collected and edited here: Hayden on Isomorphic keyboards. It would be greatly appreciated if someone would reduce and simplify his ideas, perhaps into table form.