How does interstellar matter density vary?
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.