Why is hydrogen bonding more significant than any other interaction between dipoles?
Hydrogen bonds often have a significant covalent component. This can be seen in many aspects of the hydrogen bond: it is directional, unlike Coulombic interactions, and the bond length is generally significantly shorter than predicted by Coulombic models. There is great variation in the covalent character of hydrogen bonds depending on their environment, with e.g. bond lengths between 2.2 and 4.0 Angstroms known.

Other intermolecular interactions have significant covalent components; there is nothing special about hydrogen per se but it is the most important example.