High-contrast imaging can find and characterize gas giant planets around nearby young stars and the closest M stars, complementing radial velocity and astrometric searches by exploring orbital separations inaccessible to indirect methods. Ground-based coronagraphs are already probing within 25AU of nearby young stars to find objects as small as 3M_{Jup}_. This paper contrasts near-term and future ground-based capabilities with high-contrast imaging modes of the James Webb Space Telescope (JWST). Monte Carlo modeling reveals that JWST can detect planets with masses as small as 0.2M_{Jup}_ across a broad range of orbital separations. We present new calculations for planet brightness as a function of mass and age for specific JWST filters and extending to 0.1M_{Jup}_.