I'm confused by this Q&A - I can't think of a hobbyist 3d printer design that doesn't move the build platform:
In the Printrbot it appears the print head moves in X & Z, and the build platform moves in Y. Same as the RepRap Mendel.
In the MakerBot the print head moves in Z, and the build platform in X&Y. In the Up! 3d printer the print head moves in X, build platform Y&Z. In the Ultimaker, print head X&Y, build platform Z (this is the combination that rbanffy describes.)
So that's a good bunch of possible permutations, but the build platform always moves...
The original RepRap design (Darwin) moved the print head in X and Y, and moved the build surface in Z only (downward as the print progresses).
The Ultimaker machine is based off the Darwin design, and works similarly. Ultimaker has a very lightweight printhead, so they can print incredibly fast.
I haven't seen a moving-head deposition robot that moves only the head. I think this is because the simplest way to make a 3-axis robot involves two tools/surfaces, each moving in at least 1 axis. A tool/surface that moves in all 3 axes needs to be very stiff to avoid juddering around as the machine starts and stops line segments. It's much simpler to make a 2-axis robot and a 1-axis robot, than a 3-axis robot. :)
