Hydrogen bonds - why not in HCl?
Hydrogen bonds to chlorine atoms are known. In the gas phase HCl dimers are hydrogen bonded but the bond has only about half the dissociation energy of $\ce{(HF)2}$ which has a larger electrostatic attraction energy. The adduct $\ce{HCl\cdots OH2}$ is also known and has a similar hydrogen bond energy to that of  $\ce{HOH\cdots OH2}$.

Using neutron diffraction hydrogen bonds have been studied in many crystals. From a study of many types of amino acid crystals (and derivatives thereof) the normal $\ce{HOH\cdots O}$ hydrogen bond is found to have  a range of lengths, from about 0.175 to 0.2 nm with most lengths at around 0.185 nm. The $\ce{OH\cdots Cl}$ hydrogen bond peaks about 0.2 nm with an range of $\approx \pm$ 0.05 nm. The $\ce{NH^+\cdots Cl}$ bond is longer peaking at 0.21 nm. 

Calculations (Singh &amp; Kollman, J. Chem. Phys. v83, p4033, 1985) show that the linear hydrogen bond, X-H-X, has an energy profile that is not that dissimilar to any chemical bond when energy is plotted against X to X separation. There are electrostatic attraction terms and exchange repulsion terms. These form a potential well with repulsion dominating (positive energy) at close separation of the two X atoms, a minimum energy (negative) at about 0.18 nm for water dimers, and a gradual increase in energy as the distance X - X increases reaching zero at large separation. However, there are also polarisation terms and those due to dispersion and charge transfer to take into account. These terms are all attractive and become important only at small separation of the X atoms. However, they are not insignificant and  contribute  a few tens of percentage to the total energy. The result of these terms is to move the minimum of the potential energy to smaller values that that due to exchange and electrostatic terms alone. Thus one can imagine the H atom residing in the potential energy between the two X atoms and being close to the minimum energy. Having described this ideal case,  IR spectroscopy does  indicate that in some cases the potential may have two minima rather than just one as described so the nature of these bonds is still a subject of debate.