Could dark matter compress and form black holes? Since dark matter is even more abundant than normal matter, a dark matter black hole should not be rare...right?
The problem with trying to form a black hole with dark matter is that dark matter can only weakly interact (if at all) with normal matter and itself, other than by gravity.
This poses a problem. To get dark matter concentrated enough to form a black hole requires it to increase its (negative) gravitational binding energy without at the same time increasing its internal kinetic energy by the same amount. This requires some sort of dissipative interaction between dark matter and normal matter (or itself).
The following scenario should make this clear. Suppose we have a lump of dark matter that gravitationally attracts another lump of dark matter. As the two approach each other, they accelerate and gain kinetic energy. The kinetic energy gained will be exactly enough to then separate them to a similar degree to which they started, unless some dissipative process takes place.
An example is to suppose that dark matter is weakly interacting massive particles (WIMPs). WIMPs are gravitationally drawn towards the centres of stars. If the weak interactions happen sufficiently frequently then it might be possible for them to accumulate in stars, rather than shoot through and out the other side.
It has been hypothesised that black holes could be made like this near the centre of a Galaxy, seeded by dense neutron stars. The density of neutron star matter, combined with the enhanced density of dark matter near galaxy centres could result in dark matter accumulation in the neutron stars, leading to the formation of black holes.
Once a black hole is formed then any dark matter that enters the event horizon cannot emerge regardless of what kinetic energy it gains in the process. However, there is still a problem. Material in orbit around a black hole has less angular momentum the closer it orbits. To pass inside the event horizon requires the dark matter to lose angular momentum. Normal matter does this via an accretion disc that can transport angular momentum outwards by viscous torques, allowing matter to accrete. Dark matter has almost zero viscosity so this can't happen.
So building a supermassive black hole from a smaller seed would be difficult, but forming small black holes out of neutron stars might be easier. It has been proposed that a relative lack of pulsars observed towards our own Galactic centre could be due to this process.
As pointed out by Rob Jeffries, forming a black hole (BH) from dark matter (DM) is impossible (unless there is a [hypothetical] interaction by which dark-matter can lose energy that evades all detection). Accreting DM into an existing BH is still unlikely (since DM cannot lose its excess energy and angular momentum as easily as gas), but not impossible and a small fraction of matter accreted into the supermassive BHs (SMBHs) at galactic centres was likely dark.
However, once matter has accreted into a BH, the information about its origins (dark matter or baryonic) is lost. Therefore, it makes no sense to talk about dark matter black holes: black holes don't have any property beyond their mass, spin, and charge (no-hair theorem).
This very property makes primordial black holes interesting as candidates for dark matter, since they would not violate constraints (for example from big-bang nucleosynthesis) about the amount of baryonic matter. However, AFAIK, primordial black holes are out of favour as DM candidates (for reasons beyond the scope of this answer).
Black holes are the result of mass so concentrated that gravity does not let anything out, including light. Just about the only things we know about dark matter is that it has mass and seems to only interact with ordinary matter through gravity. Since we do not know the physics of dark matter at all, it is impossible to say what processes might concentrate dark matter enough to form a black hole, but theoretically a black hole could be formed from dark matter, or even both ordinary matter and dark matter. Some theorists [footnote] even think that is exactly what super-massive black holes are.
footnote: Jeremiah P. Ostriker of Princeton University, Collisional Dark Matter and the Origin of Massive Black Holes, and Zoltán Haiman of Columbia University, The Formation of the First Massive Black Holes. Also interesting, these papers, from 2011 to now, citing Ostriker's seminal paper.