Obtaining ultracold samples of dipolar molecules is a current challenge which requires an accurate knowledge of their electronic properties to guide the ongoing experiments. Alkali hydride molecules have permanent dipole significantly larger than those of mixed alkali species and, as pointed out by Taylor-Juarros et al. [Eur. Phys. J. D 31, 213 (2004)] and by Juarros et al. [Phys. Rev. A 73, 041403 (2006)], are thus good candidates for molecule formation. In this paper, using a standard quantum chemistry approach based on pseudopotentials for atomic core representation, large Gaussian basis sets, and effective core polarization potential, we systematically investigate the electronic properties of the alkali hydrides LiH to CsH, in order to discuss general trends of their behavior. We computed (for the first time for NaH, KH, RbH, and CsH) the variation of their static polarizability with the internuclear distance. Moreover, in addition to potential curves, we determine accurate values of permanent and transition dipole moments for ground and excited states depending on the internuclear distance. The behavior of electronic properties of all alkali hydrides is compared to each other, in the light of the numerous other data available in the literature. Finally, the influence of the quality of the representation of the hydrogen electronic affinity in the approach on the results is discussed.