We analyze the properties of the circumgalactic gas (CGM) around 120 galaxies with stellar and dark matter halo masses similar to that of the Milky Way. We focus on the morphology and kinematics of the neutral hydrogen component of the CGM and how this depends on the ratio of gas-to-stellar mass within the optical radius. In gas-rich galaxies, gas temperatures rise monotonically from center of the halo out to the virial radius. Average neutral gas column densities remain higher than 10**19 atoms cm−2 all the way from the center of the galaxy out to radii of 50-70 kpc. In gas-poor galaxies with fg < 0.1, gas temperatures remain fixed at ~10^6 K from the edge of the disk out to radii of 100 kpc. The column density of neutral gas drops below 1019 atoms cm−2 at radii of 10 kpc. The neutral gas distributions are also more asymmetric in gas-poor galaxies. Most of these trends can be explained by the fact that in the Illustris simulation, gas-poor galaxies with Milky Way masses have massive (108Mo) black holes that accrete at few percent of Eddington, and that energy is being dumped into the halo at large (100 kpc) radii in the form of bubbles of hot gas in these systems. We also find that the circumgalactic gas rotates coherently about the center of the galaxy with a maximum rotational velocity of around 200 km/s. In gas-rich galaxies, the average coherence length of the rotating gas is 40 kpc, compared to 10 kpc in gas-poor galaxies. In the most gas-rich systems, the CGM can rotate coherently over scales of 70-100 kpc. We discuss our results in the context of recent observations of the CGM in low mass galaxies via UV absorption-line spectroscopy and deep 21cm observations of edge-on spiral galaxies.