X-ray diffraction, magnetic susceptibility, electron-spin resonance, and heat-capacity investigations were performed on MAl2O4 compounds with M=Co, Fe, Mn, and Zn. All compounds crystallize in cubic spinel structure AB2O4 with minor inversion between A and B sites. CoAl2O4 and FeAl2O4 reveal spin-glass-like ground states with freezing temperatures well below the Curie-Weiss temperatures indicating strong geometric frustration. Below the freezing temperatures, the heat capacities show a T2 temperature dependence for T→0K as has recently been observed in some related geometrically frustrated magnets, in contrast to the linear dependence expected for common spin glasses. The heat capacity of FeAl2O4 exhibits an additional orbital contribution. With the absence of a cooperative Jahn-Teller distortion, this points toward an orbital freezing. MnAl2O4 orders antiferromagnetically below TN=40K with a reduced value of the ordered moment and a large paramagnetic component.