We report radio SETI observations on a large number of known exoplanets and other nearby star systems using the Allen Telescope Array (ATA). Observations were made over about 19000 hours from May 2009 to Dec 2015. This search focused on narrow-band radio signals from a set totaling 9293 stars, including 2015 exoplanet stars and Kepler objects of interest and an additional 65 whose planets may be close to their Habitable Zone. The ATA observations were made using multiple synthesized beams and an anticoincidence filter to help identify terrestrial radio interference. Stars were observed over frequencies from 1- 9 GHz in multiple bands that avoid strong terrestrial communication frequencies. Data were processed in near-real time for narrow-band (0.7- 100 Hz) continuous and pulsed signals, with transmitter/receiver relative accelerations from -0.3 to 0.3 m/s^2. A total of 1.9 x 10^8 unique signals requiring immediate follow-up were detected in observations covering more than 8 x 10^6 star-MHz. We detected no persistent signals from extraterrestrial technology exceeding our frequency-dependent sensitivity threshold of 180 - 310 x 10^-26 W / m^2.