Hybrid analog and digital precoding allows millimeter wave (mmWave) systems to achieve both array and multiplexing gain. The design of the hybrid precoders and combiners, though, is usually based on knowledge of the channel. Prior work on mmWave channel estimation with hybrid architectures focused on narrowband channels. Since mmWave systems will be wideband with frequency selectivity, it is vital to develop channel estimation solutions for hybrid architectures based wideband mmWave systems. In this paper, we develop a sparse formulation and compressed sensing based solutions for the wideband mmWave channel estimation problem for hybrid architectures. First, we leverage the sparse structure of the frequency selective mmWave channels and formulate the channel estimation problem as a sparse recovery in both time and frequency domains. Then, we propose explicit channel estimation techniques for purely time or frequency domains and for combined time/frequency domains. Our solutions are suitable for both SC-FDE and OFDM systems. Simulation results show that the proposed solutions achieve good channel estimation quality, while requiring small training overhead. Leveraging the hybrid architecture at the transceivers gives further improvement in estimation error performance and achievable rates.