How does interstellar matter density vary? Answer to my question partially answers this one, about density of intergalactic matter and matter within galaxy:


  But it is mostly a hot, ionized void. How void? The density of the intergalactic medium is about 1 to 100 particles per cubic meter (you can compare it to the mean galactic density, of about a million particles per cubic meter, or that of Earth's atmosphere, of about 10^26 particles cubic meter). How hot? It can go from 10^5 to 10^7 K.


If we skip the most dense concentrations of matter (stars, planets, generally everything solid, liquid or plasma, and border conditions like their atmosphere) how dense interstellar matter can we find? What is the concentration of matter in densest nebulae that still don't collapse into bodies like planets or stars?

And conversely, how empty does the space get at its emptiest? I could imagine only very few particles in last their short moments of travel into the center exist under a black hole's event horizon, but other than that, how empty a space can be found in the universe, and where?
The interstellar medium is a multiphase medium, and you can find (some references in this lecture and in this thesis manuscript (this one is in French, but numbers are international)):


the hot ionized medium (HIM) with density as low as 10^-3 cc (particles per cubic centimeter);
the warm ionized medium (WIM), with density of the order of 0.03 cc;
the warm neutral medium (WNM), with density of the order of 0.25 cc;
the HII regions, with densities ranging from 1 to 10^4 cc;
the cold neutral medium (CNM), with density of the order of 25 cc;
the molecular clouds, with densities above 10^3 cc, up to 10^6 cc roughly.


These different phases are due to the interplay of cooling and heating processes of its own components (Wolfire et al. 1995). The lowest density regions are hot and associated to supernova expansion bubbles. The HII regions (HII for "ionized hydrodgen") are associated with O stars (massive stars that can efficiently ionized their environment).

The highest density you can get with no evidence of forming stars are of the order of 10^4 cc (see for example this talk by Ward-Thompson on starless cores). Dense, molecular clouds that are about to collapse and form a star have a density of the order of 10^6-10^7 cc.