We report the measurement of the spin-orbit angle of the extra-solar planets HAT-P-8 b , HAT-P-9 b , HAT-P-16 b and HAT-P-23 b , thanks to spectroscopic observations performed at the Observatoire de Haute-Provence with the SOPHIE spectrograph on the 1.93-m telescope . Radial velocity measurements of the Rossiter-McLaughlin effect show the detection of an apparent prograde , aligned orbit for all systems . The projected spin-orbit angles are found to be \lambda = -17 ^ { \circ } ^ { +9.2 } _ { -11.5 } , -16 ^ { \circ } \pm 8 ^ { \circ } , -10 ^ { \circ } \pm 16 ^ { \circ } , +15 ^ { \circ } \pm 22 ^ { \circ } for HAT-P-8 , HAT-P-9 , HAT-P-16 and HAT-P-23 , respectively , with corresponding projected rotational velocities of 14.5 \pm 0.8 , 12.5 \pm 1.8 , 3.9 \pm 0.8 , and 7.8 \pm 1.6 km s ^ { -1 } . These new results increase to 37 the number of accurately measured spin-orbit angles in transiting extrasolar systems . We conclude by drawing a tentative picture of the global behaviour of orbital alignement , involving the complexity and diversity of possible mechanisms .