Are there any planned experiments to intentionally create black holes in the lab for study? And if they did what kind of machine would be making them? And what would they study?
 A: It is worth stressing that black holes are predictions of classical General Relativity models. Our experimental data have established that the underlying level of nature is quantum mechanical. There is a large body of research on quantizing gravity and unifying the three forces studied with particle physics experiments with the gravitational force. String theory is successful in doing that ,  unification of all forces and quantization of gravity, although a validated model has not yet appeared, as there are thousands of possible solutions of the landscape of string theories. 
String theory introduces at least six extra dimensions which in the prevailing model proposals are curled to very small size, of the order of postulated string dimensions , (10^-33 cm) since they are unobservable in our four dimensional frame where we live and study nature. Phenomenologists exist so that they can propose measurable predictions from models, and there exist models, called large extra dimension models, which do give predictions for micro black holes that decay immediately ,  at the current energies of the LHC. These were the models which created a fuss about the LHC being dangerous, the hoi polloi not understanding the necessity of immediate decay to usual particles  for such entities..
The experiments have looked for the signatures of these micro black holes and have set limits for these models. The conclusion is that no signs of large extra dimensions have been seen up to now, but the search will go on with the new data coming now from the LHC at double the energy.
A: The smallest possible black hole that could be observed would be one with a mass on the scale of the Planck mass (~ 22 µg) and a radius on the scale of the Planck length (really small).
Thermodynamics makes it impractical to pack multiple particles into such a small space, so the best bet would be to accelerate elementary particles to have relativistic mass greater than the Planck mass, and smash them together.
A machine to accomplish that would look like the LHC, but much, much bigger. The LHC accelerates protons up to 7 TeV. Plugging that energy into $E = mc^2$, we get m = 1.25 × 10-14 µg, which is 15 orders of magnitude (a quadrillion times) too small.
It's likely that LHC-style particle accelerator technology doesn't really scale that far, so "looks like the LHC" might be a stretch.
A: In 2008 Ulf Leonhardt of University of St. Andrews UK led the first research group to make an artificial black hole. Its purpose was to look for experimental evidence of "Hawking Radition," photons and neutrinos emitted by black holes. "Hawking Radiation" couldn't be detected from astrophysical black holes because the signal would be overwhelmed by the CMB radiation. These artificial black holes were created using metamaterials that mimic astrophysical black hole behavior without needing large gravities. Artificial black holes have also been made by Chinese and American research groups.
http://www.technologyreview.com/view/415718/artificial-black-hole-created-in-chinese-lab/
http://physicsworld.com/cws/article/news/2008/mar/06/artificial-black-hole-created-in-lab
A: If we calculate the schwarzschild radius (and below is a really convenient link if you don't want to calculate yourself.
http://physics.unl.edu/~klee/flash_astro/bhole_sim010.swf
And if we look at the size of an atomic nucleus:  1.6 fm (1fm= $10^{−15}$ m=0.000000000000001 m) for a proton in light hydrogen to about 15 fm for the heaviest atoms, such as uranium.
Source:  http://simple.wikipedia.org/wiki/Atomic_nucleus
Now, I realize this is oversimplified, but even so, a black hole the size of a proton would need to have a mass of roughly 500 million tons (if I got my math right).   Any black hole they might potentially make at CERN would need to be far far far far smaller than a proton - as in, super duper tiny and whether or not that is possible depends on the laws of physics of the very very very small more than it depends on what they want to do.
Are super tiny quantum black holes dangerous? Well, there's a lot of good and probobly quite a few bad articles on that very subject because of the attention it got, but the short answer is no, they would disintegrate in a stream of particles, like everything else that's created in CERN - assuming they could be created at all.
If CERN was able to create a black hole (they probobly can't), but if they could, then, they probobly would because it's very unlikely that it would be dangerous and because it would be a new discovery.   We like new discoveries.   We learn stuff.   It provides insight into the early universe and the laws of physics for the extreme and the very very very tiny.
More powerful particle interactions happen by cosmic rays and super fast moving particles crashing into our atmosphere every day than happen in CERN.  CERN is doing nothing that doesn't happen already.   All they're doing is getting a much closer look at it.
