If dark matter only interacts with gravity, why doesn't it all clump together in a single point? I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, strong nuclear force, and electromagnetism.
Those are my understandings going in. If I'm wrong, please correct me. I've done some googling, and I haven't found anything confirming or denying that dark matter is affected by either of the fundamental nuclear forces.
So since dark matter only interacts with gravity, what causes any dark matter particle to be repelled from another? If they can pass freely through each other, and they are gravitationaly attracted to each other, why don't such particles clump together in a single 'point' in space? 
It seems to me that particles occupying a single 'space' are philosophically not distinct particles, but I don't know how actual physics would play into this.
Edit This article, author's credentials unknown, but implicitly claims to be a physicist or astronomer, says "...[P]hysicists generally take all dark matter to be composed of a single type of particle that essentially interacts only through gravity."
Edit 2 The author is this Lisa Randall, "Professor of Science on the physics faculty of Harvard University."
 A: Great question.  Observations show that Dark Matter (DM) only noticeably interacts gravitationally, although it's possible that it may interact in other ways "weakly" (e.g. in the 'WIMP' model --- linked).  Everything following has no dependence on whether DM interacts purely/only gravitationally, or just predominantly gravitationally --- so I'll treat it as the former case for convenience.
Observable matter in the universe 'clumps' together tremendously: in gas clouds, stars, planets, disks, galaxies, etc.  It does this because of electromagnetic (EM) interactions which are able to dissipate energy.  If you roll a ball along a flat surface it will slow down and eventually stop (effectively 'clumping' to the ground), because dissipative forces (friction) are able to transfer its kinetic energy away.
On the other hand, imagine you drill a perfect hole, straight through the center of the Earth, and you drop a ball down it.  (Assuming the hole and the earth are perfectly symmetrical...) the ball will just continually oscillate back and forth from each side of the earth to the other --- because of conservation of energy.  Just like a frictionless pendulum (no rubbing, no air resistance).  This is how dark matter interacts, purely gravitationally.  Even if there was no hole through the center of the earth, the DM will just pass straight through and continue to oscillate back and forth, always reaching the same initial height.  To zeroth order, dark matter can only 'clump' as much as its initial energy (obtained soon after the big-bang) allows.  One example of such a 'clump' is a 'Dark Matter Halo' in which galaxies are embedded.  DM Halos are (effectively) always larger than the normal (baryonic) matter inside them --- because the normal matter is able to dissipate energy and collapse farther.
A: At this point we know a lot more about what dark matter is not, than what it is. It does not interact via the electromagnetic force, and interaction via the strong force is also unlikely. Interaction via the weak force is still an active area of research (See here).
To understand why dark matter does not form clumps, imagine two particles of dust whizzing through space at high speed toward each other. They get close together but just narrowly avoid a head-on collision before going off in different directions. For a moment, when they were very close together, the pull of gravity between the two objects was at its strongest, but the particles were travelling too fast for the small gravitational pull to hold them together.
Now imagine a different scenario where the two dust particles collide head-on (which happens via the electromagnetic force). Now that the two particles have lost energy through heat, the gravitational pull between the particles can keep them held together in a clump. Soon, a third dust particle comes along and collides into this clump of dust, loses its kinetic energy, and becomes bound to the clump as well. As the clump of dust grows, more particles collide with it and it continues to grow larger and larger, eventually into a planet or star.
Dark matter rarely bumps into itself (or other matter), so it is almost always like the first case, rather than the second. Millions of dark matter particles are passing through you right now without hitting anything. Since it is so hard for them to get rid of their kinetic energy, they tend to not get bound up into clumps.
A: If you consider dark matter to be in the form of massive particles that have kinetic energy but only interact gravitationally, then there is a simple way to look at this.
If the particles start off in a configuration where their total energy (the sum of positive kinetic energy and negative gravitational potential energy) is zero; then they are on the cusp between being gravitationally bound or unbound.
To make things "clump" you need to make their total energy negative. The only way you can do this is to remove kinetic energy from the system.
With normal matter this is done through electromagnetic interactions, which turn the kinetic energy of normal matter (protons, electrons etc.) into photons, which then escape from the system. Since these kinds of interactions do not occur for dark matter (by definition), then there is no way to get rid of kinetic energy and so the dark matter remains as a large "halo" around gravitationally clumping ordinary matter.
A: Because the dark matter does not interact a lot, there is no mechanism that would slow it down quickly. When a dark matter particle is falling towards some gravitational center, it is speeding up, then it flies through the periapsis and continues away into the distance. Normal matter clumps into planets, because it is slowed down by interactions / collisions. Dark matter does not collide and cannot deposit energy. It stays on elliptical orbits with very large axes and there is no way how to shrink the ellipse. Normal matter can shrink its orbital path by collisions, but not dark matter.
A: Dark matter might be matter which has no protons or neutrons, more like pure energy than the kind of matter which is familiar to us ... kind of like the "GEONs" which John Archibald Wheeler proposed, speculatively, many years ago (see his book Geons, Black Holes & Quantum Foam for details).
Because it contains energy, and because energy is gravitationally equivalent to mass, it has gravitational-interactions with ordinary matter, so it provides the extra mass necessary to prevent a galaxy from flying apart as it rotates.
But, because it contains no protons or neutrons, it can't collapse down and form stars, nor can it interact with photons, for the same reason;  so it might be that the only way we can detect it is through its gravitational interactions.
A: Because on their way to that hypothetical single point, they would pass a whole load of normal matter that would disturb their journey. You can more or less take non-gravitational forces out of the equation entirely and ask the same question of normal matter. That being said, the theory goes that (ultimately) everything will end up coalescing, and dark matter would be a participant in that. It just takes a while.
