Planet
The smallest known planet is PSR B1257+12A, one of the first extrasolar planets discovered, which was found in 1992 in orbit around a pulsar. Its mass is roughly half that of the planet Mercury. The smallest known planet orbiting a main-sequence star other than the Sun is Kepler-37b, with a mass (and radius) slightly higher than that of the Moon.
Super-Earth
The smallest super-Earth found as of 2008 was MOA-2007-BLG-192Lb. The planet was announced by astrophysicist David P. Bennett for the international MOA collaboration on June 2, 2008. This planet has approximately 3.3 Earth masses and orbits a brown dwarf. It was detected by gravitational microlensing.