Shear flow instabilities are an important aspect of hydrodynamic studies. The present review article discusses the role of an ambient magnetic field which both modifies the Kelvin-Helmholtz instability and may introduce new types of magnetohydrodynamic waves and instabilities. A brief overview of magnetospheric pulsations is presented with an emphasis on the long-period resonant Alfvén waves associated with the high speed solar wind. The spatio-temporal evolution of magnetically modified shear flow instabilities in various space plasma structures is addressed. A distinction between convective and absolute instabilities is necessary for proper understanding of theory and correct interpretation of the observations. Finally, it is shown how incompressible Alfvénic disturbances may become unstable in a compressible flow in the absence of any shear. An application to coronal loops is presented.