The combined effects of Reynolds number (Re) and blockage ratio (BR) on the spatio-temporal characteristics of turbulent flow separation around rectangular cylinders with different streamwise aspect ratios (AR = 1 and 3) were investigated using a time-resolved particle image velocimetry. Five different blockage ratios (BR = 2.5%, 4%, 5%, 10%, and 15%) were examined at Reynolds numbers of 3000, 7500, and 15000. The results are analyzed in terms of the mean flow, Reynolds stresses, reverse flow area, and proper orthogonal decomposition (POD). For the AR = 1 cylinder, the results show that the wake characteristics are nearly independent of Reynolds number and blockage ratio. Spectral analyses of the velocity fluctuations reveal that the von Kármán shedding frequency is independent of Reynolds number and blockage ratio, however, the Kelvin-Helmholtz frequencies increase with increasing Reynolds number and blockage ratio. The results also show that the contributions from the first POD mode pair to the total energy increase with blockage ratio but independent of Reynolds number. The POD mode coefficients show significant cycle-to-cycle variation at lower blockage ratios. The spectra of the velocity fluctuations, reverse flow area and POD mode coefficients all show dominant peaks at the fundamental shedding frequency. For the AR = 3 cylinder, two regimes (unattached and reattached) are identified, however, the boundary between these regimes shows a complex dependency on both Re and BR. The mean flow does not reattach onto the cylinder at low Re and BR, but tends to reattach when Re and BR increase. The wake vortexes are relatively larger for the unattached test cases. The separation bubbles over and in the wake of the cylinder are dynamically coupled for cylinders in the unattached regime but independent of each other in the reattached regime. Spectral analyses of the velocity fluctuations, reverse flow area and coefficient of the first POD mode pair reveal single dominant peak at the same fundamental shedding frequency for the reattached test cases whereas multiple competing frequencies are observed for test cases in the unattached regime.