In a multi-user millimeter (mm) wave communication system, we consider the problem of estimating the channel response between the base station (BS) and each of the user equipments (UEs). We propose three different pilot training schemes/strategies, namely: 1) estimating mm wave channels separately at the UE's; 2) joint estimation of mm wave channels of all the UE's simultaneously at the BS; and 3) two stage process involving estimation at both the UE's and the BS. We propose two random constructions for the pilot/training signals/beamforming weights and analytically characterize the mutual coherence parameter of the resulting sensing matrices for one of the constructions. By exploiting the structure in mm wave channels, we develop a generalized block orthogonal matching pursuit (G-BOMP) algorithm for channel estimation in all the three strategies. Furthermore, we establish sufficient conditions for exact support recovery by the proposed G-BOMP algorithm and derive an upper bound on the norm of the channel estimation error. We also study the performance of our G-BOMP algorithm in terms of the average beamforming gain and average spectral efficiency achieved via simulations. Our results show that the proposed G-BOMP algorithm outperforms the conventional OMP algorithm and other existing multiuser mm wave channel estimation techniques. G-BOMP also performs comparable to the computationally expensive compressive estimation using Newton 's refinement technique, for the first pilot training strategy in which the UE's estimate the channels separately.