Based on a new sample of 355 quasars with significant optical polarization and using complementary statistical methods, we confirm that quasar polarization vectors are not randomly oriented over the sky with a probability often in excess of 99.9%. The polarization vectors appear coherently oriented or aligned over huge (∼ 1 Gpc) regions of the sky located at both low (z ∼ 0.5) and high (z ∼ 1.5) redshifts and characterized by different preferred directions of the quasar polarization. In fact, there seems to exist a regular alternance along the line of sight of regions of randomly and aligned polarization vectors with a typical comoving length scale of 1.5 Gpc. Furthermore, the mean polarization angle θ̄ appears to rotate with redshift at the rate of ∼30° per Gpc. The symmetry of the the θ̄ - z relation is mirror-like, the mean polarization angle rotating clockwise with increasing redshift in North Galactic hemisphere and counter-clockwise in the South Galactic one. These characteristics make the alignment effect difficult to explain in terms of local mechanisms, namely a contamination by interstellar polarization in our Galaxy. While interpretations like a global rotation of the Universe can potentially explain the effect, the properties we observe qualitatively correspond to the dichroism and birefringence predicted by photon-pseudoscalar oscillation within a magnetic field. Interestingly, the alignment effect seems to be prominent along an axis not far from preferred directions tentatively identified in the Cosmic Microwave Background maps. Although many questions and more particularly the interpretation of the effect remain open, alignments of quasar polarization vectors appear as a promising new way to probe the Universe and its dark components at extremely large scales.